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Question

The equation of the ellipse, whose length of the major axis is 20 and foci are (0,±5), is

A
x210+y253=1
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B
x225+y2100=1
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C
x275+y2100=1
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D
x210+y225=1
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Solution

The correct option is C x275+y2100=1
Since the foci are on yaxis, the major axis will be along the yaxis. So, equation of the ellipse is of the form
x2a2+y2b2=1(b>a).

Given,
Length of major axis 2b=20
b=10

and be=5
b2e2=25b2a2=25a2=75

Hence, the equation of the ellipse is
x275+y2100=1.

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