How do I find the Fermat Equation for a parabola in optics?

[CaptainQuaser]

I need to find a Fermat Equation for a parabola that sends light from a point sour ce on X the access back parrallell to the x access.

Thanks

If you want to see what I tried, I posted a pic a few days ago, under the title optics, but no one responded at that point.

 

[HallsofIvy]

Okay, you know it's a parabola. Do you know that the "standard" form for a parabola is y= 4cx² where (0, c) is the focus? Since you want the focus on the x-axis and want the ray back parallel to the x-axis, you need to swap x and y:
x= 4cy².

 

[CaptainQuaser]

Yes, I know, but I need the fermat equation where the Optical Path Length (OPL) is equal for all points of the surface. What I am unsure about is if the OPL for the center must be added the the OPL of arbitrary X position for the parabola, eg
N1 (So + So - X) = N1 (X^2 + y^2)^1/2, where So is the distance from the point source to the parabolic axis on the x axis, and X and Y are cooresponding arbitraray co-ordinates to points on the parabola.