# find the lines that are (a) tangent and (b) normal to the curve at the given point x^2 + xy - y^2 = 1

122,340 results

### 12th grade calculus

find the lines that are (a) tangent and (b) normal to the curve at the given point x^2 + xy - y^2 = 1

### Math

Given that x²cos y-sin y=0 ,(0,π): a)verfiy that given point is on the curve. b)use implicit differentiation to find the slope of the above curve at the given point. c)find the equation for tangent and normal to the curve at that point.

### Math

. Given that x²cos y_sin y=0,(0,π). A. Verify that the given points on the curve. B.use implicit differention to find the slope of the above curve at the given point. C.find the equation of tangent and normal to the curve at that.

### Calculus AB

Could someone please help me with these tangent line problems? 1) Find the equation of the line tangent to the given curve at the indicated point: 3y^3 + 2x^2 = 5 at a point in the first quadrant where y=1. 2) Show that there is no point on the graph of x^2 - 3xy + y^2 = 1 ...

### Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive? Negative? Zero? 2) Find an equation of the tangent line to the oven curve at the specified point. Sketch the curve and the...

### math

1 A particle is moving in a stright line with the position at any time t is given by s= t³–9t²+3t+1,where s in meters and t in second. Find its position and acceleration when velocity is ¯24m/s 2. Given that x²cos y_sin y=0,(0,π). A. Verify that the given points on the ...

### Ap Calc AB

Find the equation of the line normal to the curve at (0,0). (Normal lines are perpendicular to the tangent lines) 2y + sinx = xcoxy I found the derivative to be (cosy - cosx)/ (2+ xsiny) then the slope tangent is 0...then the slope perpendicular is undefined...so then is the ...

### maths

given the equation of the curve as y=8-2x^2 (a) find equations of tangent and the normal to this curve at the point where x=a. (b) find the value of a for which this tangent is parallel to the line with equation 3x-y+6=0

### math

how do i do this. find the equation for the lines that are tangent and normal to the curve y= (square root of 2)(cosx)at the point (pi/4, 1)

### cal

Equations of the tangent lines to hyperbola xy=1 that pass through point (-1,1) I know the graph of y=1/x but not sure about the tangent lines at given point. Are the lines tangent to (1,1) and (-1,-1)? You're correct, the graph is y=1/x, so find y' to get the slope at any ...

### Math

In this problem we consider drawing some straight lines which form a nice pattern. Consider joining the point (0.1,0) to the point (0,0.9) by a line segment; then joining (0.2,0) to (0,0.8) by a line segment; and so on. In general, consider joining the points (a,0) and (0,b) ...

### Calculus

Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write an equation for the normal line to the ...

### elementary differential geometry

Suppose that all the tangent lines of a regular plane curve pass through some ﬁxed point. Prove that the curve is part of a straight line. Prove the same result if all the normal lines are parallel.

### Calculus

(A) Find the equations of the tangent lines to the circle x^2 +y^2=25 at the points where x=4. (B) Find the equations of the normal lines to this circle at the same points. (The normal line is perpendicular to the tangent line at that point.) (C) At what point do the two ...

### math

the tangent yo the curve y=x^2 +5x -2 @ the point (1,4)intersect the normal to the same curve @ the point (-3,-8) at the point P.Find the coordinates of point P.[ans: -1/3,-16/3] just give me some hint to calculate this solution.

### Calc I

Find an equation of the tangent to the curve at the given point. y=4(sinx)^2 point: pi/6,1) So I took the derivative of the original function to get: y' = 8cosx*sinx I then chose a point to plug in to find a point for the slope. i picked pi/6 because i thought it would be ...

### calculus

Calculate the equation of the tangent and normal lines for the curve f(x) = tan 2x, at the point where the x-coordinate is: x = π/8.

### calculus

Given that x3-axy+3ay2=3a3 Find the equations for the tangent and normal lines at point (a,a)

### Calculus

I found part B, but stuck on part A. Use implicit differentiation to find the points where the parabola defined by x^2-2xy+y^2+4x-8y+24= 0 has horizontal and vertical tangent lines. A) The parabola has horizontal tangent lines at the point(s): B)The parabola has vertical ...

### Calculus

The line that is normal to the curve x^2=2xy-3y^2=0 at(1,1) intersects the curve at what other point? Please help. Thanks in advance. We have x2=2xy - 3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 + 2xy - 3y2 = 0 ? I'll suppose it's the second ...

### math calc. asap asap please

the point on the curve is 4y=x^2 nearest to (7,2) is: this is what i did: i solved for y and I know that the there's a tangent line at (x1,y1). so using y-y1=m(x-x1), I found the lines of the tangent and perpendicual lines: slope is derivative so it is 1/2x1 tangent: y-y1=.5x1...

### calculus

Find an equation of the tangent(s) to the curve at a given point. Then graph the curve and the tangent(s). x = 6sin(t), y = t^2 + t; (0,0) How do I do this without the value of t? I don't see a way to eliminate the parameter.

### calculus

1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this curve with slope equal to the slope at (2, 1)

### Calculus Help Please!!!

--- Find the slope m of the tangent to the curve y = 4 + 4x^2 − 2x^3 at the point where x = a. ---- Find equations of the tangent lines at the points (1,6) and (2,4). (1,6) Y(x)= (2,4) Y(x)=

### math

Given the equation of a closed curve is x^2-2x+4y^2+16y+1=0.Find the coordinates of the two points where the lines tangent to the curve are vertical.

### Calculus

Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points on the curve where y equals 0 and show that the tangent lines there are parallel. Find the coordinates of all points on the curve where there is a horizontal tangent line, with work.

### Precalculus

1. Consider the curve y=x^2. a. write down (dy)/(dx) My answer: 2x The point P(3,9) lies on the curve y=x^2. b. Find the gradient of the tangent to the curve at P. My answer: 2*3=6 c. Find the equation of the normal to the curve at P. Give your answer in the form y=mx+c. My ...

### calculus

Find equations of the tangent line and normal line to the curve at the given point. y = x^4 + 2e^x, (0,2)

### calculus

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent point is far from the y-axis, the line ...

### Math- Calc 1

1. At what point does the normal line to the curve x^2 - XY + Y^2 = 3 at the point (1,1) intersect the curve again? 2. Find the constants A, B so that if Y = Asin X = B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points om he graph of Y - e^x - e...

### Math- Calc 1

1. At what point does the normal line to the curve x^2 - XY + Y^2 = 3 at the point (-1,1) intersect the curve again? 2. Find the constants A, B so that if Y=A*sin X + B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points on he graph of Y = e^x - e...

### calculus

Consider the curve given by the equation y^3+3x^2y+13=0 a.find dy/dx b. Write an equation for the line tangent to the curve at the point (2,-1) c. Find the minimum y-coordinate of any point on the curve. the work for these would be appreciated i don't need the answers.

### Calc

1. At what point does the normal line to the curve x^2 - XY + Y^2 = 3 at the point (-1,1) intersect the curve again? 2. Find the constants A, B so that if Y=A*sin X + B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points on he graph of Y = e^x - e...

### Business Statistics

In each case, sketch the two speciﬁed normal curves on the same set of axes: a A normal curve with m 20 and s 3, and a normal curve with m 20 and s 6. b A normal curve with m 20 and s 3, and a normal curve with m 30 and s 3. c A normal curve with m 100 and s 10, and a ...

### calculus

find an equation of the tangent line to the curve at the given point. graph the curve and the tangent line y=x/x-1 at (2,2) )

### calculus

Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve at point P. Find the x – and y – ...

### Calculus

I have a two part question that pertains to a curve (r(x)) and its tangent line at x=3. We are given that at x=3, r(x)=8. In order to find the slope of the tangent line, we are given another point (on the tangent line): (3.2, 8.5). Therefore the slope of the tangent line at x=...

### Maths

The tangent to the curve 2y= 2x^2 -5x +4 at the point where x=1 is parallel to the normal to the curve y= ax^2 + bx +10 at the point (-2,2). Calculate the values of a and b. The answers are a=1, b=6

### AP Calculus

Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-2x)/(8y-3x) b) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y-coordinate of P. c) Find the value of d^2y/dx^2 (second derivative) at the ...

### 12th grade calculus

find the lines that are tangent and normal to th ecurve at the point given 1. 2xy+piesiny=2pie (1, pie/2) 2. x^2cos^2y-siny=0 (0, pie)

### calculus

Two lines through the point(1,-3) are tangent to the curve y=x2. Find the equations of these two lines and make a sketch to verify your results. Thank you

### Calculus - Maths

I got a few questions. Hope ya'll can help out. 1) for F(X) = 6x - 2x^2 Find the gradient of the chord joining the point where the X coorinates are 1 and (1+h) respectively. b) hence find the gradient at x=1 2) Find the Coordinates of the point on the curve Y=1/2x^3 - 3/2x^2 +...

### 12th Grade Calculus

1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3 - 9x + 5 at the point (3,5) [* for a. the answer that I obtained was y-5 = -1/18 (x-3) ] b.) What is the smallest slope on the curve? At what point on the curve does the curve have this slope? c.) ...

### Calculus

Lines tangent to the curve y-1=2x^2+3x pass through the point A(2,-1). Find the x-coordinate(s) of the point(s) of tangency. The answer is 2+2^1/2, 2-2^1/2, I just don't know how to get there. Please help! Thank you!

### calculus

find equations of the tangent lines to the curve y=x/(x+5) that pass through the point (2,7).

### calculus

Find the slope of the tangent line to the curve (sqrt(4x+y))+(sqrt(3xy)) at the point (3,4) The slope of the tangent line to the curve at the given point is ? I got -((1/2)+4sqrt(36))/((1/8)+3sqrt(36))

### calc

The slope of the tangent to the curve y=f(x) is given by (1/9)(x^2)(y^2). The curve passes through the point (3,1). Find the value of y when x=3*cubedroot(3).

### Calculus

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2+7 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent point is far from the y-axis, the line ...

### math

With regards to question J: The variables x and y are connected by the equation y = x2 - x - 5. Some corresponding values of x and y are given in the table below. x -4 -3 -2 -1 0 1 2 3 4 5 y 15 7 a -3 -5 b -3 1 7 15 (a) Calculate the values of a and b (b) Use 2 cm to represent...

### Calculus - Damon

Find the line which passes through the point (0, 1/4) and is tangent to the curve y=x^3 at some point. So I found the derivative which is 3x^2. Let (a, a3) be the point of tangency. 3x^2 = (a3 - 1/4)/(a-0) I'm not sure how to solve for a. Yes, the point is (0,1/4) but it's not...

### Calculus

a)The curve with equation: 2y^3 + y^2 - y^5 = x^4 - 2x^3 + x^2 has been linked to a bouncing wagon. Use a computer algebra system to graph this curve and discover why. b)At how many points does this curve have horizontal tangent lines? Find the x-coordinates of these points. I...

### calc

for the parametric curve defined by x=3-2t^2 and y=5-2t ...sketch the curve using the parametric equation to plot of the point. use an arrow to indicate the direction of the curve for o<t<1. Find an equation for the line tangent to the curve at the point where t=-1. x=3...

### Math

Show that the tangent to the curve 25x^5+5x^4-45x^3-5x^2+2x+6y-24=0 at the point (-1,1) is also a normal at two points of the curve.

### Please check my maths?

How should i do this question?? it says: find the equation of the tangent to the curve y=(x-2)^3 at the point (3,1). calculate the coordinates of the point where this tangent meets the curve again. I know how to get the first part, if i'm not wrong, it's y = 3x - 8 but no ...

### Help Calc.!

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P.

### please help; calc

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P.

### calculus

A curve passes through the point (1,-11) and it's gradient at any point is ax^2 + b, where a and b are constants. The tangent to the curve at the point (2,-16) is parallel to the x-axis. Find i) the values of a and b ii) the equation of the curve

### math

(a) Integrate wrt x:(〖2x〗^4- x^2+2)/x^2 (b) The gradient of the tangent at a point on a curve is given by x2 + 2x – 2. Find the equation of the curve if it passes through (2,3).

### Calc AB

Suppose that f(x) is an invertible function (that is, has an inverse function), and that the slope of the tangent line to the curve y = f(x) at the point (2, –4) is –0.2. Then: (Points : 1) A) The slope of the tangent line to the curve y = f –1(x) at the point (–4, 2) ...

### Calculus

Could someone please help me with this question; Find the tangent to the curve y=x^2-8x+14 which slope is -2. Show that this tangent touches the curve y= -x^2-4x+4. Find the point of contact. Thank you.

### calculus

Notice that the curve given by the parametric equations x=25−t^2 y=t^3−16t is symmetric about the x-axis. (If t gives us the point (x,y),then −t will give (x,−y)). At which x value is the tangent to this curve horizontal? x = ? At which t value is the tangent to this ...

### Tangent Lines-Calculus

a line is tangent to the curve y= (x^2 + 3)/ (x+3)^1/2 at the point where x=1. write the equation of this line i get y= 3x-1 yet it's wrong. please explain thank you

### AP AB Calculus

Linear approximation: Consider the curve defined by -8x^2 + 5xy + y^3 = -149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,-1) c. There is a number k so that the point (4.2,k) is on the curve. Using the tangent line found in part (b), ...

### Calculus

Find an equation of the tangent line to the curve at the given point. (Assume the tangent line form to be f(x) = mx + b.) y= e^x/x (1,e) I got m= 0 nd b=e could anyone tell if its right?

### maths

find equations for the tangent and the normal at P (1n2, 2k) on the curve with equation y=ke^x, where k is a constant. (b) given that y=sin^-1x, show that (1-x^2)d^2y/dx^2-xdy/dx=0

### maths

find equations for the tangent and the normal at P (1n2, 2k) on the curve with equation y=ke^x, where k is a constant. (b) given that y=sin^-1x, show that (1-x^2)d^2y/dx^2-xdy/ dx=0

### Calculus

The slope of the tangent to a curve at any point (x, y) on the curve is -x/y . Find the equation of the curve if the point (3,-4) on the curve.

### last calc question, i promise!

given the curve x + xy + 2y^2 = 6... a. find an expression for the slope of the curve. i got (-1-y)/(x + 4y) as my answer. b. write an equation for the line tangent to the curve at the point (2,1). i got y = (-1/3)x + (5/3). but i didn't any answer for c! c. find the ...

### math

Find two point on a circle x^2+y^2=1 where the slope of the tangent line is -2 write the equation for the normal lines at these points.

### Need help fast on calc

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P. -when plugging y as 2 in original, it ...

### Calculus

For the parametric curve defined x=2t^3-12t^2-30t+9 and y=t^2-4t+6 ..find dy/dx and then where is the tangent to the curve vertical (give the cartesian coordiantes of the points. and find the tang. to the curve horizontal dx/dt= 6t^2-24t-30 dy/dt= 2t-4 dy/dx= (t-2)/(3t^2-12t-...

### Calculus

Use the given equation to answer the following questions. (Enter your answers from smallest to largest.) r = 8cos(¦È) 0 ¡Ü ¦È < ¦Ð (a) Find the points on the given curve where the tangent line is horizontal. theta= theta= (b) Find the points on the given curve where...

### Maths

Point P in the curve y=x^3 has coordinates (3,27) and PQ is the tangent to the curve at P.Point Q touches the x-axis.Find the area of the region enclosed between the curve, PQ and the x-axis. My answer: I used differenttiation to find the gradient of the tangent: dy/dx=3x^2. ...

### Math

Find the equation for the tangent line to the curve at the point defined by the given value of t.also find d²y/dx² at this point x=SECt, y=TANt,where t=π/4.

### Math

Find the equation for the tangent line to the curve at the point defined by the given value of t.also find d²y/dx² at this point x=SECt, y=TANt,where t=π/4.

### calculus

Consider curve given by x^2+ 4y^2= 7 + 3xy.. Three part question A) show that dy/dx = 3y-2x/8y-3x B) Show that there is a point P with x-coordinate 3 at whiich the line tangent to the curve at P is horizontal. Find the y-coordinate of P. C) find the value of d^2y/ dx^2 at the ...

### maths --plse help me..

if tangent to the curve y=2sinx +sin2x are drawn at p(x=60degree) then find the area of the quadrilateral formed by the tangent the normal at P and the coordinate axis

### equation on tangent of a curve need help

find the equation of a tangent of a curve at point(1,3) x^2.y^3+y^2.x^4+4x^2-14=0,i tried differentiate it n also applying this formula y=mx+b.bt i gt confuse

### calculus

f(x)=kx^2+3 a) if the tangent lines to the graph of f at (t,f(t)) and (-t, f(-t)) are perpendicular, find t in terms of k b) Find the coordinate of the point of intersection of the tangent lines mentioned in part (a) in terms of k

### calculas

Find the equations for the tangent line and normal line to the curve for f(x)=(x^4)+(2e^x) at the point (0,2)?

### math

f(x) = 4e^-1x +13x +5 at (0,9) 1. All steps for finding the first derivative of the function are clearly and accurately shown. 2. All steps for evaluating the derivative to find the slope of the tangent to the curve at the given point are clearly and accurately shown. 3. All ...

### calculus

Find an equation of the tangent line to the curve at the given point. y = 3x^2 - x^3, (1,2)

### calculus

Find an equation of the tangent line to the curve at the given point. y= (9x)/(x+1)^2 P = (0,0)

### Calculus

Find an equation of the tangent line to the curve at the given point y^2 = x^3 (2-x) (1,1)

### calculus

Find an equation of the tangent line to the curve at the given point. y^2=x^3 (2-x) (1,1)

### Calculus 1

Find an equation of the tangent line to the curve at the given point. y =(1+2x)^12, (0,1)

### Math, Calc

Use implicit differentiation to find an equation of the tangent line to the curve at the given point x^2+2xy+4y^2=12. Point (2,1). (Eclipse)

### math

For the curve given by 4x^2+y^2=48+2xy, show that there is a point P with x-coordinate 2 at which the line tangent to the curve at P is horizontal.

### Calculus 1

The curve y = |x|/(sqrt(5- x^2)) is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (2, 2)

### Calculus

the curve: (x)(y^2)-(x^3)(y)=6 (dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3)) a) find all points on the curve whose x-coordinate is 1 and write an equation for the tangent line of each of these points b)find the x-coordinate of each point on the curve where the tangent line is vertical

### Calculus

If F(x)=x^3−7x+5, use the limit definition of the derivative to find FŒ(5), then find an equation of the tangent line to the curve y=x^3−7x+5 at the point (5, 95). FŒ(5)= The equation of the tangent line is y = x + . Check your answer for yourself by graphing...

### Maths

I need some help with my maths questions please! What angle does the tangent to the curve y=x^4-x^3+7x make with the positive direction of the x-axis at the point where x=2? Find any x values for which the gradient of the tangent to the curve y=x^2-3x-1 is parallel to the line...

### Calculus 1

The curve y =|x|/(sqrt(5−x^2)) is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (2,2).

### math

Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the point (0, −25). Find the coordinates of the points where these tangent lines intersect the parabola.

### Calculus

The graph of the equation x2 − xy + y2 = 9 is an ellipse. Find the lines tangent to this curve at the two points where it intersects the x-axis. Show that these lines are parallel.

### Calculus

Draw a diagram to show that there are two tangent lines to the parabola y=x^2 that pass through the point (0,-4). Find the coordinates of the points where these tangent lines intersect the parabola. So far I have taken the derivative and got y'=2x.. Using point slope form I ...

### calculus

Find an equation of the tangent line to the curve at the given point y = x + cosx, (0,1)

### calculus

find the equation of the tangent line to the given curve at the indicated point x^2(y^2)=(y+1)^2 (4-y^2) at (0,-2)

### calculus

find tangent line equation to the curve at the given point: y= 7e^x cos(x) P=(0,7)