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
$\displaystyle y'=2x$
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).
$\displaystyle slope = \frac{a^{2} + 3}{a-1}$
Set this equal to 2a and solve for a.
Good luck!!