Question

Find the equation of locus of a point equidistant from $A(2,0)$ and the $Y-$ axis.

Answer 1

Let the point be $P(h,k)$

Given,

$P$ is equidistant from $A(2,0)$ and the $Y$ axis

$\Rightarrow \sqrt{{(h-2)}^2+K^2}=h$

$\Rightarrow {(h-2)}^2+K^2=h^2$ [Squaring]

$\Rightarrow h^2+4-4h+K^2=h^2$

$\Rightarrow K^2=4(h-1)$

Replacing $(h.k)$ with $(x,y)$ we get

$y^2=4(x-1)$