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Question

The curve described parametrically by x=t2+t,y=2t−1 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 B Parabola
x=t2+t and y=2t1

By elimination of t

t=y+12
x=(y+12)2+y+12

y2+4y4x+3=0
On comparing with ax2+by2+2hxy+2gx+2fy+c=0

we have a=0,b=1,g=2,f=2,h=0,c=3
Δ=abc+2fghaf2bg2ch2=40
and h2ab=0h2=ab
So, the given equation is a parabola

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