# Parabola

• Mar 20th 2011, 09:18 PM
thamathkid1729
Parabola
Find an equation that says that
P = (x, y) is equidistant from F = (2, 0) and the y-axis.

• Mar 20th 2011, 09:49 PM
pickslides
An equation or find the point P?

If the later what about (1,0)?
• Mar 20th 2011, 11:34 PM
thamathkid1729
I need to find an equation, not just 1 point. I know that (1,0), (2,2), and (2,-2) are all equidistant from F = (2, 0) and the y-axis
• Mar 21st 2011, 05:23 AM
HallsofIvy
Since you title this "parabola", I suspect you already know the answer. However, the derivation is this:

The distance from (x, y) to (2, 0) is $\sqrt{(x- 2)^2+ y^2}$ and the distance from the (x, y) to the y-axis is simply x. To be equidistant, we must have $\sqrt{(x-2)^2+ y^2}= x$

Square both sides and simplify.