# Thread: Lines Tangent to a Parabola

1. ## Lines Tangent to a Parabola

Find equations of both lines through the point (2,-3) that are tangent to the parabola $\displaystyle y = x^2 + x$.

I know the derivative of the parabola: $\displaystyle y' = 2x + 1$, but I am not sure how to use that to find the two lines.

2. The trick with this is they don't tell you where it's tangent.

Use $\displaystyle y-y_{1}=m(x-x_{1})$

Where $\displaystyle y=x^{2}+x, \;\ y_{1}=-3, \;\ m=y'=2x+1, \;\ x_{1}=2$

Then solve for x. You will get two solutions. Those are the x-coordinates of your tangency points.