# 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.

1. 👍 0
2. 👎 0
3. 👁 44
1. dy/dx = 2x + 5
slope of tangent at (1,4) = 2(1) +5 = 7
at (1,4) ...
4 = 7(1) + b
b= -3
tangent equation at (1,4) is y = 7x - 3

at (-3,-8)
slope of tangent is 2(-3) + 5 = -1
so slope of normal is +1
equation of normal is y = x + b
at (-3,-8) , -8 = -3 + b
b = -5
equation of normal is y = x - 5

where do they intersect ?
when 7x - 3 = x - 5
6x = -2
x = -1/3
back into y = x-5 , (or the other equation, makes no differencen)
y = - 1/3 - 5 = -1/3 - 15/3 = -16/3

so the two straight lines intersect at (-1/3, -16/3)

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### 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 =

asked by Lynn on February 25, 2015
2. ### 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 =

asked by Lynn on February 24, 2015
3. ### 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 =

asked by Anonymous on February 25, 2015
4. ### maths

The parabola y2 = 4ax, where a > 0, and the rectangular hyperbola xy = C2, where C > 0, intersect at right angles. Show that the tangent and normal to either curve at the point of intersection meet the x-axis at T and N where TN =

asked by lia on March 23, 2011
5. ### 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 +

asked by Jen on October 15, 2006
6. ### 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

asked by Annie on October 30, 2016
7. ### 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

asked by Abdullah11 on March 23, 2017
8. ### 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

asked by Annie on November 25, 2016
9. ### 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

asked by Claire on April 4, 2008
10. ### 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

asked by jun on January 24, 2011

More Similar Questions