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Question

The curve described parametrically by x=5cost and y=2sint represents

A
Circle
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B
Parabola
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C
An ellipse
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D
Hyperbola
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Solution

The correct option is C An ellipse
x=5cost,y=2sint

cost=x5(1)
sint=y2(2)

Squaring (1) and (2) and then adding both

(x5)2+(y2)2=1
x225+y24=1
4x2+25y2100=0
On comparing with

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

We have a=4,b=25,h=0,g=0,f=0,c=100

Δ=abc+2fghaf2bg2ch2=100000
and h2<ab
So, its an ellipse.

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