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Question

If x=3(cost+sint); y=2(costsint) represents a conic, then its foci are

A
(±10,0)
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B
(±13,0)
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C
(0,±13)
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D
(0,±10)
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Solution

The correct option is A (±10,0)
x=3(cost+sint); y=2(costsint)
x3=cost+sint (1)
y2=costsint (2)

Now, squaring and adding equation (1) and (2), we get
x29+y24=2(sin2t+cos2t)
x218+y28=1
a2=18, b2=8(a>b)
e=1b2a2
e=1818
e=1018
foci are (±10,0)

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