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Question

The curve described parametrically by x=sin2t,y=2cost represents

A
Circle
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B
Parabola
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C
An elipse
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D
Hyperbola
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Solution

The correct option is B Parabola
x=sin2t,y=2cost

On Squaring y

y2=4cos2t
cos2t=y24(1)
sin2t=x(2)

Adding (1)and (2)

x+(y2)2=1
4x+y24=0

On comparing with

ax2+by2+2hxy+2gx+2fy+c=0

We have , a=0,b=1,h=0,g=2,f=0,c=4

Δ=abc+2fghaf2bg2ch2=4
and h2=ab

So, it represents a parabola

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