Question

Find the equation to the locus of a point $P$ from which the distance to $(2,0)$ is equal to the distance from $P$ to the $y$-axis.

Answer 1

$\sqrt{(x-2{)}^2+(y-0{)}^2}=|x|$

$(x-2{)}^2+y^2=x^2$

$x^2-4x+4+y^2=x^2$

$y^2=4x-4$

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