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Question

The curve represented by x=3(cost+sint),y=4(costsint) is

A
Ellipse
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B
Parabola
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C
Hyperbola
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D
Circle
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Solution

The correct option is A Ellipse
Given x3=cost+sint & y4=costsint

Squaring these two,

x29=1+2sint.cost...(i)

y216=12sintcost....(ii)
Adding (i) & (ii)

x29+y216=2x218+y232=1

So the equation represents ellipse.

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