Question

Slanted Ellipse and something about implicit differentiation (comments)...

Answer 1

The implicit diff. part isn't so tough, it is the rest I don't much understand! Thanks.

Answer 2

to find horizontal tangents, plug in 0 for y' in the implicit differentiation

Answer 3

the question is asking for the greatest y-coordinate of the ellipse. the line y=ymax is a horizontal tangent.

Answer 4

similarly, to find vertical tangents, plug in 0 for x' in the implicit differentiation of x(y)