Find a polar equation for the conic Ellipse with its focus at the pole and the given vertex or vertices (2 , 0) , (8 ).
Given:
Vertices (2, 0) and
To determine:
Polar equation for the conic ellipse with the focus at its pole:
Solution:
The given vertices imply that the directrix is vertical and is to the right of the pole:
And,
Polar equation is in the form:
Now,
Let's find the center of both the vertices:
So,
The center is located at the mid-point of the vertices:
Now,
The length of the major-axis is the distance between the two vertices, 2a
From the given:
The distance from the center to the focus is c:
Therefore,
The eccentricity is :
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