Question

The parametric equation of parabola $(y-2{)}^2=12(x-4)$ is

• A. $x=4-3t^2,y=2-6t$
• B. $x=2+3t,y=4+t^2$
• C. $x=4+3t^2,y=2+6t$
• D. $x=2+3t^2,y=4+6t$

Answer 1

The correct option is C $x=4+3t^2,y=2+6t$

Given: Equation of parabola $(y-2{)}^2=12(x-4)$
On comparing with standard form $(y-k{)}^2=4a(x-h)$
$\Rightarrow a=3,h=4,k=2$

Parametric equation of $(y-k{)}^2=4a(x-h)$ are given by
$x-h=a{t}^2,y-k=2at$

Hence the parametric equations for $(y-2{)}^2=12(x-4)$ are given by
$x-4=3t^2,y-2=6t$
$\Rightarrow x=4+3t^2,y=2+6t$