Parabola, tangebt line and Normal Line intersect

[mrm0607]

Homework Statement

Where does the normal line to the parabola y= x - x^2 at the point (1,0) intersect the parabola a second time? Illustrate with a sketch

Homework Equations

y= x - x^2

The Attempt at a Solution

y' = 1-2x

slope of tangent = -1 (after substituting value of x in above eq)

-ve reciprocal of (-1) = 1

equation of normal line is

y - 0 = 1 (x -1)

y = x -1

After this I am not sure how to find the second point of intersection.

I understand there has to be one since parabola is symmetric about its axis.

Thank you.

 

[w3390]

You've done everything correct so far. You now have a separate equation and you want to find where it intersects the parabola. By setting the equations equal, you will get your point of intersection.

 

[mrm0607]

Thank you