Question

Find a polar equation of the conic with its focus at the pole.

Conic                                          Vertex or Vertices

Ellipse                                          (2, 0),  (10, π)

Answer 1

Step 1:

The vertices of the ellipse is and .

In polar form, the equation of an ellipse with a focus at origin is .

Substitute in the above polar equation.

Substitute in the above polar equation.

Step 2:

Divide equation (2) by equation (1).

Substitute in equation (1).

Step 3:

Substitute and in .

Solution :

The polar equation of the ellipse is .