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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?

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

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