Hello, fogel1497!

We are expected to know (or be able to derive) this formula:

. . .[1]

Differentiate implicitly: . .[2]Given: .

Substitute [2] into [1]: .

Multiply top and bottom by

Since we have: . .

. . and we have: .

The tangent line is horizontal when(a) Find the points on the curve where the tangent is horizontal.

So we have: .

Horizontal tangents when: .

The tangents line is vertical when is undefined.(b) Find the points on the curve where the tangent is vertical.

So we have: .

Vertical tangents when: .