Question

The parametric equation of the parabola $(x-1{)}^2=-12(y-2)$ is

• A. $x=6t,y=2-3t^2$
• B. $x=1+6t,y=2-3t^2$
• C. $x=1+6t,y=2+3t^2$
• D. $x=6t,y=3t^2$

Answer 1

The correct option is B $x=1+6t,y=2-3t^2$

Here, parabola is of form $(x-h{)}^2=-4a(y-k)$
$\because 4a=12\Rightarrow a=3,$
parametric equation is
$\Rightarrow y-k=-a{t}^2\Rightarrow y-2=-3t^2$
$\Rightarrow x-h=2at\Rightarrow x-1=6t$
$\Rightarrow x=1+6t,y=2-3t^2$