Let A(2,3) be a fixed point. A point P moves such that PA is equal to the distance of P from the y-axis. Find the equation of the locus of P

Question

PA2 = (x-x1)^2 + (y-y1)^2 +???
= (x-2)^2 + (y-3)^2 +???

I tried solving it using the distance formula but I'm still confused because I am given only one point A (2,3) coordinate. I searched all blogs on google but couldn't find a solved problem similar to this. Please help!

Answer 1

Ths distance of (x,y) from the y-axis is just x. So,

√((x-2)^2 + (y-3)^2) = x
(x-2)^2 + (y-3)^2 = x^2
x^2-4x+4 + (y-3)^2 = x^2
(y-3)^2 = 4x-4
(y-3)^2 = 4(x-1)

as I showed using the properties of parabolas