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Question

Find the parametric equation of the parabola x24x32=12y


Your Answer
A
x=3+6t, y=23t2 
Your Answer
B
x=26t, y=3+3t2
Your Answer
C
x=6t, y=3t2
Correct Answer
D
x=2+6t, y=33t2

Solution

The correct option is D x=2+6t, y=33t2
x24x32=12y
x24x+4432=12y
(x2)2=12(y3)
Comparing the given equation with X2=4aY
a=3, X=x2,  Y=y3

Parametric form for X2=4aY is
X=2at,Y=at2
Put X=x2, Y=y3
x2=2atx=2+2atx=2+6ty3=at2y=3at2y=33t2

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