I have two problems dealing with this. I am getting myself all screwed up and could use help.

the first is at what points is the slope of the tangent line equal to 1 on [x^2/9] + [y^2/16] = 1

So I got the derivative dy/dx = -[16x/9y]

so now I solve for -[16x/9y] = 1 ; correct?

The other question is find the points at which the tangent is horizontal for

x^3 + 4x^2 +xy^2 - 4y^2 = 0

I got dy/dx = [3x^2 + 8x +y^2]/6

so same thing, solve for dy/dx to be zero?