Find an equation that says thatP= (x, y) is equidistant fromF= (2, 0) and they-axis.

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- Mar 20th 2011, 08:18 PMthamathkid1729ParabolaFind an equation that says that
*P*= (*x, y*) is equidistant from*F*= (2, 0) and the*y*-axis.

- Mar 20th 2011, 08:49 PMpickslides
An equation or find the point P?

If the later what about (1,0)? - Mar 20th 2011, 10:34 PMthamathkid1729
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, 04:23 AMHallsofIvy
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 $\displaystyle \sqrt{(x- 2)^2+ y^2}$ and the distance from the (x, y) to the y-axis is simply x. To be equidistant, we must have $\displaystyle \sqrt{(x-2)^2+ y^2}= x$

Square both sides and simplify.