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Questions  

Which of the following parametric equation does
not represent a parabola

a
x=t2+2t+1,y=2t+2
b
x=at2−2t+1,y=2at−2a
c
x=3sin2⁡t,y=6sin⁡t
d
x=asin⁡t,y=2acos⁡t

detailed solution

Correct option is D

x=aT2,y=2aT represents a parabola.in(a) a=1,T=t+1, in (b) a=a,T=(t−1)in(c) a=3,T=sin⁡t. But in (d)if 2aT=2acos⁡t⇒ T=cos⁡t which does not satisfy x=aT2

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