$\"\"$

The polar equation of the conic is $\"\"$ .

A conic is an ellipse only when $\"\"$ .

When $\"\"$ is close to zero, the ellipse is circular.

Graph:

Graph the equation $\"\"$ for $\"\"$ and $\"\"$ . \ \

$\"\"$

Observe the graph:

The ellipse is nearly circular when $\"\"$ is close to $\"\"$ and becomes more elongated as $\"\"$ .

At $\"\"$ , the curve becomes a parabola.

$\"\"$

Graph:

Graph of the equation $\"\"$ for $\"\"$ and $\"\"$ . \ \

$\"\"$

The ellipse is nearly circular when $\"\"$ is close to $\"\"$ and becomes more elongated as $\"\"$ .

At $\"\"$ , the curve becomes a parabola.