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find the parametric equation of the line that is tangent to the parabola y=x^2 at the point(-2 , 4)

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  1. clculus

    find the parametric equation of the line that is tangent to the parabola y=x^2 at the point(-2 , 4)

  2. calculus

    find the parametric equation of the line that is tangent to the parabola y=x^2 at the point(-2 , 4)

  3. 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

  5. Calc.

    Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis. I don't really get what this question is asking. It looks like the area of right triangle to me...try the graph, and shade the area under

  6. Math

    If f(x)=3x^2-5x, find the f'(2) & use it to find an equation of tangent line to the parabola y=3x^2-5x at the point (2,2). My ans is f'(2)=7 & y=7x-12. What is parabola exactly? & is the any possibility if the eqtn of f(x) is not the same with parabola

  7. maths

    Find parametric equations of the line that is tangent to the parabola y = x^2 at the point (−2, 4).

  8. math

    Consider the parabola y = 6x − x2. (a) Find the slope of the tangent line to the parabola at the point (1, 5). 4 (b) Find an equation of the tangent line in part (a). y =

  10. calculusiii

    he paraboloid z = 4 − x − x2 − 2y2 intersects the plane x = 4 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (4, 2, −24). (Enter your answer as a comma-separated list of equations. Let x,

  11. Calc.

    sketch the curve using the parametric equation to plot the points. use an arrow to indicate the direction the curve is traced as t increases. Find the lenghth of the curve for o

  12. Calc

    The slope of the tangent line to the parabola y=4x2–3x+5 at the point where x=–5 is: (-43) The equation of this tangent line can be written in the form y=mx+b where m is: (-43) and where b is:_____________?

  13. calculus

    The slope of the tangent line to the parabola y=4x2–6x+6 at the point where x=5 is: The equation of this tangent line can be written in the form y=mx+b where m is: and where b is:

  15. 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

  16. math

    I need help with parametric equations, locus problems, tell me how to solve all questions if you can. Need help with one below: Tangents are drawn to a parabola x^2=4y from an external point A(x1,y1) touching the parabola at P and Q (a) Prove that the mid

  17. Calculus

    a) Find a Cartesian equation relating and corresponding to the parametric equations: x=2sin(3t), y=9cos(3t). Write your answer in the form P(x,y)=0, where P(x,y) is a polynomial in x and y, such that the coefficient of y^2 is 4. b)Find the equation of the

  18. math help

    find the equation to the tangent line of the parabola given by x^2=2y at point (3, 9/2)

  20. maths

    consider the line y=6x-k and the parabola y=x^2 i) for what value of k is the line y=6x-k a tangent to the parabola y=x^2 ? ii) the line y=6x-k intersects the parabola in two distinct places. what is the largest integer value that k can take ?

  21. Vectors

    3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the cartesian equation for the plane @ parallel to $ and containing the point (1,1,2) (ii)Calculate the distance between $ and @ (b)(i)Find the parametric equations for the line of

  22. vectors

    3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the cartesian equation for the plane @ parallel to $ and containing the point (1,1,2) (ii)Calculate the distance between $ and @ (b)(i)Find the parametric equations for the line of

  23. cal

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8 find the equation of the tangent lines at x=1 and x=-2 graph the quadratic

  25. Math

    Find the parabola with equation y = ax^2 + bxwhose tangent line at (2, 12) has the equation y = 14x − 16

  26. Pre-Calculus

    Im having trouble with this. Find an equation of the tangent line to the parabola at the given point and find the x-intercept of the line. x^2=2y (4,8)

  27. maths

    find the gradient of the tangent to the parabola y=4x-x^2 at (0,0) hence calculate the size of the angle between the line y=x and this tangent. (as i cant show you the diagram all that it shows is the line going through (0,0) and having one point of

  28. Calculus

    Sketch a graph of the parabola y=x^2+3. On the same graph, plot the point (0,−6). Note there are two tangent lines of y=x2+3 that pass through the point (0,−6). The tangent line of the parabola y=x^2+3 at the point (a,a^2+3) passes through the point

  30. calc

    The slope of the tangent line to the parabola y=4x2–3x+5 at the point where x=–5 is:______ The equation of this tangent line can be written in the form y=mx+b where m is:_________ and where b is:______? The first to blanks are -43, but what is b?

  31. precalc

    find an equation of the tangent line to the parabola at the given point..show work y=(-2)x^2 (-1,-2)

  32. Pre-Cal

    Find an equation of the tangent line to the parabola at the given point, and find the x-intercept of the line. 17) x^2=2y , (-3,9/2) 18) y=-2x^2 , (-1,-2)

  33. math vector

    Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P. r(t)=ti+t^(2)j+tk, P(0,0,0)

  35. calculus I

    Problem: Consider (1) the parabola y=3-1/10 x^2 and (2) the upper half of the circle centered at (20, 0) with radius of 10. Find the points on the parabola where the tangent line is also tangent to the upper half of the circle. (You can find these points

  36. Parametric derivatie help plz

    Find the equation of the line tangent to the parametric curve define by x=cos2t and y=sin3t and t=pi/12 plz i don't no where to start from show working

  37. calculus 2

    Find the area of the region bounded by the parabola y = 5x^2, the tangent line to this parabola at (3, 45), and the x-axis.

  38. calculus 2

    Find the area of the region bounded by the parabola y = 3x^2, the tangent line to this parabola at (1, 3), and the x-axis.

  40. calculous

    Find the area of the region bounded by the parabola y = 4x^2, the tangent line to this parabola at (4, 64), and the x-axis.

  41. calculous

    Find the area of the region bounded by the parabola y = 4x^2, the tangent line to this parabola at (4, 64), and the x-axis.

  42. calculus

    Find the area of the region bounded by the parabola y=x^2 , the tangent line to this parabola at (10, 100), and the x-axis.

  43. Calculus

    Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 5 ln t, y = 8sqrt(t), z = t^5 (0,8,1) (x(t),y(t),z(t))=( )

  45. math

    Consider the parabola y = 6x − x2. (a) Find the slope of the tangent line to the parabola at the point (1, 5)

  46. math

    Consider the parabola y = 7x - x2. (a) Find the slope of the tangent line to the parabola at the point (1, 6). 1

  47. Calc 2

    Find the area of the region bounded by the parabola y = 5x2, the tangent line to this parabola at (5, 125), and the x-axis. its not 625/3

  48. Calc 3

    Find the parametric equations for the tangent line to the curve with the given parametric equations at specified point. x= e^t y=te^t z=te^(t^2) (1,0,0)

  50. Calc 3

    Find the parametric equations for the tangent line to the curve with the given parametric equations at specified point. x= e^t y=te^t z=te^(t^2) (1,0,0)

  51. Math (Calculus) (mean value theorem emergency)

    Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c in the interval (-2,4)

  52. Calculus II

    Hi, not sure how to set this integral up for my Calculus II homework. "Given a graph that contains a parabola and a line, the equation of the parabola is x=(y-3)²/4 and the equation of the line is y=6-x. Find the area of the shaded region". Are we

  53. Math

    Let f(x) be the parabola -x^2+16x-16. find the point (x,y) on f such that tangent line to f at (x,y) passes through the origin. My ans is (8,48). First i do f'x then i find x and lastly i find y. I do this because the max/min point is the point where

  55. Calculus

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

  56. calculus

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8

  57. Parametric Curve

    Match the parametric curve to its description. Be careful: It is possible that the same description fits more than one parametric curve! (a) (t + 1,4t−2) (b) (t^2,3t^2) (c) (cost,2(cost)^2 + cost) (d) ((2t + 1)sint,(2t + 1)cost) (e) (2t−1,5) (1) A

  58. precalculus

    graph the parabola y=2x^2-6x-3. plot point on the parabola A[1,-7] and draw a line through A with an angle of inclination equal to 30 degrees. then find the equation of the line and its second point of intersection B, with the parabola

  60. Calculus

    Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=4cos(t) y=4sin(t) z= 10cos(2t) (2sqrt2,2sqrt2,0)

  61. 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

  62. Calculus

    Great! I understand now that C0=f(a) c1=f'(a) c2=f"(a)/2 Now, If I am to find the parabolization of the equation x^2-x at x=2, then c0=x^2-x=2^2-2=2 c1=2x-1=2(2)-1=3 c2=2/2=1 So, the equation (taken from c0+c1(x-a)+c2(x-a)^2) is >> 2+3(x-2)+1(x-2)^2?? Is

  63. 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.

  65. math

    Given the parametric curve x= sin(2t) and y=2 sin(t)+ sin(2t) 1) Calculate the slope of the tangent line at any value of t. 2) Find the tangent line at t= (1/2)(Pi).

  66. pre cal

    Write the equation of the tangent line to the parabola y^2=-1/2x at the point (-1,-2)

  67. calculus

    The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)-9 at point P and the parabola y=4x^(2)+4x+5 at point Q. a. If a line tangent to the cubic at point P is parallel to the line tangent to the parabola at point Q, find the value of c where c>0.

  68. math

    The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)-9 at point P and the parabola y=4x^(2)+4x+5 at point Q. a. If a line tangent to the cubic at point P is parallel to the line tangent to the parabola at point Q, find the value of c where c>0.

  70. math

    can u help this the qustion is : A circle passes through the points (1,4)&(5,0) and its centre lies on the line x+y-3=0.Find (i) the equation of the circle and it parametric equations . (ii) the centre,diameter and area of the circle . (iii) the equation

  71. steev

    can u help this the qustion is : A circle passes through the points (1,4)&(5,0) and its centre lies on the line x+y-3=0.Find (i) the equation of the circle and it parametric equations . (ii) the centre,diameter and area of the circle . (iii) the equation

  72. calculus

    Consider the function below. f(x) = 4x2 - 5x (a) Find f '(2). (b) Use the answer in part (a) to find an equation of the tangent line to the parabola y = 4x2 - 5x at the point (2, 6). y =

  73. Math

    I have a series of questions that I did. They lead up to the last question I can't solve. Could you check my math and help me with the last question? Thanks! a) Let a be the point (2,3). Compute the distance from Origin 0 to A answer: a^2 + b^2 = c^2 3^2 +

  75. math

    Use implicit differentiation to find the equation of the tangent line to the curve xy3+xy=14 at the point (7,1) . The equation of this tangent line can be written in the form y=mx+b i don't seem to no how to find m or b

  76. calculus

    5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the secant line on the interval [1,

  77. Calculus

    Find the equation of a TANGENT line & NORMAL line to the curve of x^2+y^2=20such that the tangent line is parallel to the line 7.5x – 15y + 21 = 0

  78. Calculus

    I am unsure of how to take the derivative of this equation. It may be the exponents that are giving me trouble but I'm not sure exactly. Find the equation of the tangent line to the curve 4e^xy = 2x + y at point (0,4). On the left side, is the "xy" the

  80. Calculus

    1. use the definition mtan=(f(x)-f(x))/(x-a) to find the SLOPE of the line tangent to the graph of f at P. 2. Determine an equation of the tangent line at P. 3. Given 1 & 2, how would I plot the graph of f and the tangent line at P if : f(x)=x^2 +4,

  81. Math

    Suppose f(x)=5/(x-2). f'(5)=-5/9. Use this to find the equation of the tangent line to the curve y=5/x-2 at the point (5,(5/3)). write your answer in the form y=mx+b where m is the slope and b is the y-intercept. The equation of the tangent line is.....

  82. Math (equation of tangent line)

    Consider the implicit equation 2xy-1=(x+y+1)^2 a) Compute and solve for the derivative dy/dx as a function of x and y. b) Find the equation of the tangent line to the graph of the above when y=-1. For part a, I found the derivative being equal -(x+1)/(y+1)

  83. calculus

    -find the equation of the tangent line to the curve y=5xcosx at the point (pi,-5pi) -the equation of this tangent line can be written in the form y=mx+b where m= and b= -what is the answer to m and b?

  85. Calculus. I need help!

    HARDER PARTS WAS 3(x^2+y^2)^2=26(y^2+y^2) Find the equation of the tangent line to the curve (a lemniscate) 3(x^2+y^2)^2=26(y^2+y^2) at the point (-4,2). The equation of this tangent line can be written in the form y=mx+b where m is:? and where b is:?

  86. math calculus

    Use implicit differentiation to find the equation of the tangent line to the curve xy^3+2xy=9 at the point (31). The equation of this tangent line can be written in the form y=mx+b where m is

  87. calc

    Find an equation of the tangent line to the curve at the given point. y = 6 x sin x P= (pi/2 , 3pi) i know the slope of a tangent line is equal to the first derivative. For that I got 6xcosx + 6sinx but idk how to put that into the y-y1=m(x-x1) formula to

  88. 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

  90. Calculus 1

    Find the equation of the tangent line to the curve y=6xcosx at the point (pi,-6pi) The equation of this tangent line can be written in the form y=mx+b What is m ? What is b ?

  91. Calculus

    Find the equation of the tangent line to the curve y=2sinx at the point ((pi/6), 1). The equation of the tangent line can be written in y=mx+b form, where m=sqrt3. What is b?

  92. math

    Find the equation of the tangent line to the curve y=5xcosx at the point (pi,–5pi). The equation of this tangent line can be written in the form y=mx+b where m= and b=

  93. COLLEGE CALCULUS.

    Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=5 at the point (4,1) . The equation of this tangent line can be written in the form y = mx+b where m is:? and where b is:?

  95. calculus

    If f(x)=4x^(5/2), find f'(4) Use this to find the equation of the tangent line to the curve y=4x^(5/2) at the point (4,f(4)) . The equation of this tangent line can be written in the form y=mx+b where m is______ and where b is _____

  96. Calculus

    If f(x)=(3x)/(1+x^2) find f′(4). Use this to find the equation of the tangent line to the curve y=3x1+x2 at the point (4,0.70588). The equation of this tangent line can be written in the form y=mx+b where m is: and where b is:

  97. Calculus

    Find the equation of the tangent to the curve at x = 3 for the parametric equations below: x= t+1/t y= t^2+1/t^2, with t>0 a) y= 2x+1 b) y= 6x-11 c) y= 6x-39 d) y= 2x-1

  98. 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.

  100. calculus

    Use implicit differentiation to find an equation of the tangent line to the curve. sin(x+y)=4x−4y at the point (π,π). Tangent Line Equation:

  101. math

    Find the equation of the tangent line to the curve y=6tanx at the point (pi/4,6). The equation of this tangent line can be written in the form y=mx+b where m is: and where b is:

  102. calculus

    Use implicit differentiation to find an equation of the tangent line to the curve sin(x+y)=2x−2y at the point (π,π). Tangent Line Equation:

  103. Calculus

    Find an equation for the tangent line of the function y=x+(4/x) at the point (2, 4). The equation of the tangent line is . You may enter the equation in any form.

  105. Calc 3

    Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x^2 + y^2 and the ellipsoid 6x^2 + 5y^2 + 7z^2 = 39 at the point (−1, 1, 2)

  106. Calculus

    1) An equation of the line contains points (7/9, 7) and (-7/9) is 2) Find the slope of the line tangent to the curve y=x^2 at the point (-0.6, 0.36) and find the corresponding equation of the tangent line

  107. calculus

    To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (64, 8), we know that (64, 8) is a point on the line. So we just need to find its slope. The

  108. Calculus

    A function f(x) is defined by: f(x) = { m * sinx + n, if x 2 pi. a. Given that f(x) is a differentiable function, find the values of m and n. b.Write the equation of the tangent line to f(x) at x = 2pi. c. Use the tangent line equation to find an

  110. Mathematics

    Use implicit differentiation to find the points where the parabola defined by x2−2xy+y2−4y+4=0 has horizontal and vertical tangent lines. The parabola has horizontal tangent lines at the point(s) (x-y)/x-y+2 . The parabola has vertical tangent lines at

  111. math

    f(t) = t^2 − 1 Find the equation of the line tangent to the graph of f(t) at t = 5. Enter the equation of the tangent line here (in terms of the variable t): y =

  112. Math

    Find the equation of the tangent line to the curve: 2(x^2+y^2)^2 = 25(x^2-y^2) at the point ( 3 , 1 ). The equation of this tangent line can be written in the form y = mx+b

  113. calculus

    f(t) = − 4 t2 − t− 6 Find the equation of the line tangent to the graph of f(t) at t = 8. Enter the equation of the tangent line here (in terms of the variable t):

  115. math

    f(t) = t2 − 1 Find the equation of the line tangent to the graph of f(t) at t = 5. Enter the equation of the tangent line here (in terms of the variable t): y =

  116. Math please help!

    Find the equation of the tangent line to the curve: 2(x^2+y^2)^2 = 25(x^2-y^2) at the point ( 3 , 1 ). The equation of this tangent line can be written in the form y = mx+b

  117. Calculus

    Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface r(u,v) =(2u, 3u^2+5v, -4v^2) at the point (0,-10,-16)

  118. Calculus

    Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface r(u,v) =(2u, 3u^2+5v, -4v^2) at the point (0,-10,-16)

  120. ap calc

    Consider { a sin x + b, if x ≤ 2π { x^2 - πx + 2, if x > 2π A.) Find the values of a and b such that g(x) is a differentiable function. B.) Write the equation of the tangent line to g(x) at x = 2π. C.) Use the tangent line equation from Part B to

  121. Calculus

    find the slope of the tangent line to the parabola y=x^2+3x at the point (-1, -2) using lim x-->a (f(x)-f(a))/x-a

  122. math

    Find the values of a,b, and c if the parabola y=a(x^2)+bx+c is tangent to the line y=-2x+3 at (2,-1) and has a critical point when x=3

  123. calculus

    Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.f(x)= x^2 - 5x +2 (1, -2)

  125. MATH

    Find an equation of the tangent plane to the given parametric surface at the specified point. r(u, v) = u cos vi + u sin vj + vk; u = 7, v = π/3

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