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Question

An ellipse is drawn by taking the diameter of the circle (x-1)2+y2=1as its semi-minor axis and the diameter of the circlex2+(y-2)2=4 as the semi-major axis, if the center of the ellipse at the origin and its axis are the coordinates axes, then the equation of the ellipse is


A

4x2+y2=4

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B

x2+4y2=8

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C

4x2+y2=8

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D

x2+4y2=16

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Solution

The correct option is D

x2+4y2=16


Explanation for the correct option:

Find the equation of the ellipse :

Given the circle(x-1)2+y2=1

Radius =1 and diameter =2

Length of semi-minor axis =diameter of the circle (x-1)2+y2=1(given)

b=2

And Circle x2+(y-2)2=4

Radius =2 and diameter =4

length of the semi-major axis =diameter of the circle x2+(y-2)2=4 (given)

a=4

Therefore the equation of the ellipse

x2a2+y2b2=1x242+y222=1x216+y24=1x2+4y2=16

Hence the correct option is D.


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