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# Bisecting an ellipse Let R be the region in the First ISBN: 9780321570567 2

## Solution for problem 51RE Chapter 10

Calculus: Early Transcendentals | 1st Edition

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Problem 51RE

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.

Step-by-Step Solution:

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

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##### ISBN: 9780321570567

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