Question

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

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

review the definition of a parabola.

The standard equation is

y^2 = 4px

if the focus is at (p,0) and directrix x = -p

So, you have to shift your axes giving you

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

see

http://www.wolframalpha.com/input/?i=parabola+(y-3)%5E2+%3D+4(x-1)