# Find equations of tan and normal lines to parabola

• Jan 28th 2013, 10:42 AM
togo
Find equations of tan and normal lines to parabola
I was going to write the whole thing out but I'll just take a picture haha.

This is the second time working the problem a couple hours in and another set of eyes would probably help

Question: Find equations of the tangent and normal lines to the parabola with vertex (0,3) and focus (0,0 where x = -1
(I did not attempt the normal part of the calculation yet)

answer s/b tan line: 2x - 12y + 37 = 0

http://i50.tinypic.com/30krasg.jpg
• Jan 28th 2013, 01:11 PM
HallsofIvy
Re: Find equations of tan and normal lines to parabola
Well, to begin with, the equation of your parabola is wrong. The vertex is at (0, 3) and the focus is at (0, 0). The focus is below the vertex so the parabola opens downward. The equation of the parabola is $\displaystyle y= -\frac{1}{12}x^2+ 3$.

Now, y'= -(1/6)x so that, at x= 1, the slope of the tangent line is -1/6. What is the equation of a line with slope -1/6 through (1, 35/12)?

For the normal line, the slope is the negative reciprocal of the tangent line. What is the equation of a line with slope 6 through (1, 35/12)?