Conic equation given vertices and focus?

Question

Find a polar equation for an ellipse with a focus at the pole (0,0) and the given polar coordinate as the endpoints of its major axis:
(1.5,0) and (6,pie)

Answer 1

Given that focus (0 , 0)

The endpoints of the major axis are (1.5 , 0) and (6 , pie)

Major axis is

Now ecentricity e

General equation of polar co-ordinates

Substitute e value

Substitute the values in general equation of polar co-ordinates

Therefore the required polar equation of an ellipse is