Question

The parametric equations of the parabola $y^2-4 x-8 y-12=0$ are

• A. $x=7+2 t, y=-4+t^2$
• B. $x=-7+2 t, y=4+2 t$
• C. $x=-7+t^2, y=-4+2 t$
• D. $x=-7+t^2, y=4+2 t$

Answer 1

Answer: (D)

Given equation of parabola,
$y^2-4 x-8 y-12=0$
or $y^2-8 y+16=4 x+28$
$(y-4)^2=4(x+7)$
Comparing with $Y^2=4 a X$
$Y=y-4, a=1, X=x+7$
parametric form of $Y^2=4 a X$
$ X=a t^2, Y=2 a t $
$ \Rightarrow x+7=t^2, y-4=2 t$
or $x=-7+t^2, y=4+2 t$