The equation of the ellipse, whose length of the major axis is 20 and foci are (0,±5), is
A
x210+y25√3=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 Cx275+y2100=1 Since the foci are on y−axis, the major axis will be along the y−axis. 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=25⇒b2−a2=25⇒a2=75
Hence, the equation of the ellipse is x275+y2100=1.