Question

I need to check my work. It is from a "fake" AP Calculus AB 2008 exam.

The line normal to 3x^2+4y+y^2=3

at x = m is parallel to the y-axis. What is m? the choices for the answers are

a. 3
b. -2
c. 0
d. -3
e. 2

I used implicit differentiation to get a derivative of

dy/dx = (-6x)/(4+2y)

Won't the slope of the normal line be the neg. recip of this derivative function?

This means

(4+2y)/(6x)

To be parallel to the y-axis, the slope is undefined so 6x = 0 and x = 0.

This means choice c is correct?

Answer 1

Agreed. Looks correct.

Answer 2

I didn't do any of the math, but I read your method and it sounds just perfect.
Derive to get the slope, solve for dy/dx.
The line normal to this will be the negative reciprocal.
For it to be parallel to the y axis, it would have to be undefined. So yeah.
Or you could have just known that the line normal would be parallel when the tangent was 0 and solved it that way without taking the negative reciprocal. Both work.

Answer 3

Okay, and yeah. I went ahead and checked your implicit differentiation too. That checks out.