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Question

The curve represented by the parameters x=t2+1 and y=2t+1 is

A
a parabola
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B
a circle
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C
a hyperbola
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D
an ellipse
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Solution

The correct option is A a parabola
Given parameters are
x=t2+1t2=x1 (1)y=2t+1t=y12 (2)
From (1) and (2),
x1=14(y1)2y22y4x+5=0
Now comparing it with general form of conic, we get
a=0,b=1,h=0,c=5,g=2,f=1
Now, Δ=0+0040=40
and h2=0=ab
Hence, given conic represents a parabola.

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