Question

The point $S$ is $(3,0)$ and the abscissa of the point $M$ is $-3.$ A variable point $P$ is such that,ordinates of $P$ and $M$ are equal. Find the equation of locus of $P$ such that $SP=PM$

Answer 1

$S(3,0)$

Let $M(-3,a)$ and $P(l,a)$

Given $SP=PM$

$\sqrt{(l-3{)}^2+(a-0{)}^2}=\sqrt{(l+3{)}^2+(a-a{)}^2}$

$(l-3{)}^2+a^2=(l+3{)}^2$

$a^2=(l+3^2)-(l-3^2)$

$a^2=4.l.3=12l$

Since $P(l,a)$ and $a^2=12l$

We have the locus as $y^2=12x$