# Math Help - tangent lines

1. ## tangent lines

find the x coordinate of all the points on the parabola y=x^2 where the tangent lines pass through the point (1,-3)

2. Originally Posted by valvan
find the x coordinate of all the points on the parabola y=x^2 where the tangent lines pass through the point (1,-3)
The derivative function is

$y'=2x$

so, slope at point (a, a^2) is going to be 2a.

The slope of the tangent line can also be measured as rise over run between the points (a, a^2) and (1, -3).

$slope = \frac{a^{2} + 3}{a-1}$

Set this equal to 2a and solve for a.

Good luck!!

3. ok thanks i got x= -1 and 3