Question

The equation of the parabola with the focus $(3,0)$ and directrix $x+3=0$ is:

• A. $y^2=2x$
• B. $y^2=3x$
• C. $y^2=6x$
• D. $y^2=12x$

Answer 1

The correct option is D $y^2=12x$

Using definition of parabola, $PS=PM$

Where$S$ is the focus, $M$ is directrix and $P$ is any point on parabola, Let's Suppose $P$ be $(x,y)$
$\Rightarrow P{S}^2=P{M}^2$
$\Rightarrow (x-3{)}^2+(y-0{)}^2={\left|\frac{x+3}{\sqrt{1^2+0^2}}\right|}^2$
$\Rightarrow x^2-6x+9+y^2=x^2+6x+9$
$\Rightarrow y^2=12x$