Lines Tangent to a Parabola

**topher0805** · February 22nd 2008, 03:49 PM

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

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

**galactus** · February 22nd 2008, 04:08 PM

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

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

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

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

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