The equation of the parabola with the focus $(3,0)$ and the directrix $x+3=0$, is.
The equation of the parabola with the focus $(3,0)$ and the directrix $x+3=0$, is.
$y^2=3 x$
$y^2=6 x$
$y^2=12 x$
$y^2=2 x$
Solution
Given that focus is $S(3,0)$, let $P(x, y)$ be any point on the parabola.
$\therefore$ Directrix is, $x+3=0$
Also, $S P^2=P M^2$
$
\begin{aligned}
& \Rightarrow \quad(x-3)^2+(y-0)^2=\left(\frac{x+3}{\sqrt{1}}\right)^2 \\
& \Rightarrow \quad(x-3)^2+y^2=(x+3)^2 \\
& \Rightarrow \quad y^2=(x+3)^2-(x-3)^2 \\
& \Rightarrow \quad=(x+3+x-3)(x+3-x+3) \\
& \Rightarrow \quad y^2=2 x 6=12 x
\end{aligned}
$