Finding equations of tangent lines

[Vay]

My homework question is:

 

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

b) Show that there is no line through the point (2, 7) that is tangent to the parabola. (Is it because the point (2, 7) is "inside" the parabola, and any line radiating through that point would intersect through the parabola?)

Edited February 27, 2012 by Vay

[DrRocket]

My homework question is:

 

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

b) Show that there is no line through the point (2, 7) that is tangent to the parabola. (Is it because the point (2, 7) is "inside" the parabola, and any line radiating through that point would intersect through the parabola?)

 

 

So, what have you done to try to solve these problems ?

[Vay]

I just did it, apparently my teacher knew this question might be too hard and so she sent an email to every student with keys on solving it. Basically she told me to turn the two tangent points to the parabola that pass through (2, -3), into arbitrary point (a, a^2+a), or in terms of the original equation, (x, x^2+x). I found the derivative of (a, a^2+a) from point (2, -3), and I made that equal to the first derivative of x^2+x(slope). The result, after solving for 0, were two numbers, meaning two slopes. I used the point slope formula to establish the two slopes into equation form, and that was the answer.

 

1. y= -x-1

2. y= 11x-25

Edited February 27, 2012 by Vay