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 $x=4+3t^2,y=2+6t$

Here, parabola is of form $(y-k{)}^2=4a(x-h)$
$\because 4a=12\Rightarrow a=3,$
parametric equation is
$\Rightarrow x-h=a{t}^2\Rightarrow x-4=3t^2$

$\Rightarrow y-k=2at\Rightarrow y-2=6t$
$\Rightarrow x=4+3t^2,y=2+6t$