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Question

The area of the ellipse x216+y225=1 is

A
16π
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B
20π
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C
25π
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D
36π
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Solution

The correct option is B 20π
Given,

x216+y225=1

take y=0

we get, x=±4

ellipse cuts the x-axis at (4,0),(4,0)

y225=1x216

y2=25(1x216)

y=±5452x2

Area of ellipse =2× area of function y=±5452x2

A=44ydx=445452x2dx

=[54{x252x2+252sin1x5}44]

=54[{425242+252sin145}{4252(4)2+252sin145}]

Upon solving the above equation, we get,

=54(40π5)

=10π

Area of ellipse =2×10π=20π

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