f'(a) = 2a + 1
And the slope of the line between the point (a, a^2 + a) and (2, -3) is (a^2 + a + 3)/(2 - a) = 2a + 1
Can you solve that?
I'm struggling with this one problem from my text book.
"Find the equations of the tangent lines to the parabola y=(x^2)+x that pass through the point (2, -3)."
I know how to find the derivative (2x+1) and then I can find one set of points (5,30) but I can't figure out how to find the other set of points.
Thanks for your help!
The slope, m, of the line tangent to the parabola when x = p is . (this from your derivative)
The slope, m, of the line passing through points (p, r) and (2, -3) is given by
Plug the in the earlier results for r & m into this. Solve for p. (There will likely be two answers.) You then have the x value(s) for the intersection of the tanget line, with the parabola.
A quadratic equation may have, of course, two roots so there may be two tangent lines that pass through (2, -3).