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Question

The curve described parametrically by x=t2+t,y=2t1 represents 
  1. Parabola 
  2. An ellipse 
  3. Hyperbola 
  4. Circle 


Solution

The correct option is A 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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