Question

Let the equation of parabola, whose focus is $(3,0)$ and directrix is $x+5=0$ be $y^2=k(x+m)$. Find $m$?

Answer 1

Using definition of parabola

If $P(x,y)$ is a point on the parabola and $S$ is focus,

$P{S}^2=P{M}^2$
$\Rightarrow (x-3{)}^2+y^2=(x+5{)}^2$
$\Rightarrow y^2=16(x+1)$