Bisecting an ellipse Let R be the region in the First quadrant bounded by the ellipse x2/a2 + y2/b2= 1. Find the value of m (in terms of a and b) such that the line y = mx divides R into two subregions of equal area.

Solution 51REStep 1:In this problem we need to find the value of m (in terms of a and b) such that the line y = mx divides R into two subregions of equal area.Let R be the region in the First quadrant bounded by the ellipse Suppose the line divides R into two subregions of equal area.We know, the area of first quadrant of the ellipse is the area of the subregion of equal area is …(1)Step 2:Now solve for :Also we have Step 3:Therefore the region of integration is given by,By (1), the value of the area integral is Therefore,Area