math
posted by rob .
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.

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 = x5 , (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)
Respond to this Question
Similar Questions

Please check my maths?
How should i do this question?? it says: find the equation of the tangent to the curve y=(x2)^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, 
math
find the eqt. of tangent to the curve y=x^2+2x10 @ the point where the curve cuts the yaxis.[ans:y=2x10] how do i do this because they didn't give me the point...? 
math
find the coordinates of the point where the tangent to the curve y=x^3 +x +2 at the point (1,4) meets the curve again. [ans:2,8] pls help me i don't understand the question.... 
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 … 
calculus
Consider the curve defined by 2y^3+6X^2(y) 12x^2 +6y=1 . a. Show that dy/dx= (4x2xy)/(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 … 
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? 
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? 
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? 
Calculus AB
Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x1)e^x. For which value of x is the slope of the tangent line to f positive? 
Math
Given that x²cos ysin 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 …