Provide an appropriate response.Consider the curves corresponding to polar equations of the form where Explain how the graph changes as a changes. Identify any values of a for which the basic shape of the curve changes.

Question

What will be an ideal response?

Answer 1

For 0 < a < 1, the curve is an oval. As a ? 1^-, the oval develops a dimple. When  the graph resembles a parabola with a dimple at the vertex. When  the curve has two parts that resemble the branches of a hyperbola, although the left-hand "branch" has a loop and, as a increases, the right-hand "branch" develops a bulge.