Consider a standard ellipse:
where and are the lengths of semi-major and semi-minor axes respectively.
Now, consider a circle concentric with the ellipse and the radius equal to the length of the semi-major axis of the ellipse, i.e. ,
A set of complimentary points are defined on these two conics, and with a parameter, . Point is lies on the ellipse and on the circle.
The points are defined as :
Given, the pairs of complimentary points namely () , () and () with parameters , and , i.e., the points on the ellipse are , and .
Find the ratio of the area of the triangle to that of the triangle .
Details and Assumptions: