Question

Find equations of both lines through the point (1, -2) that are tangent to the parabola y = x^2 + x.

Answer 1

You want the point (x,x^2+x) such that y'=2x+1 and
(x^2+x+2)/(x-1) = 2x+1
x = -1,3
So find y and y' at each of those values, and then use the point-slope form for the lines.