Find equation for shape of reflecting surface

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To derive the equation of the reflecting surface using Fermat's Principle, consider a point light source located at (d, 0) emitting parallel rays along the x-axis. The reflecting surface must be shaped to ensure that all rays reflect toward the source, which requires determining the optimal path that minimizes travel time. The key is to apply the principle of least time, leading to the formulation of the surface equation based on the geometry of reflection. The discussion seeks confirmation on the approach and clarity on the mathematical representation of the surface. Overall, the focus is on establishing the correct equation for the reflecting surface that aligns with the principles of optics.
CaptainQuaser
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Here is the question, I just need verification, don't know how to make the fancy formulas here so bear with me...

Consider a reflecting surface that produces parallel rays from a point source of light. The axis of the mirror lies on the x-axis which passes through the mirror at x=y=0. The source is at x = d, y=0 and rays of light are produced paralled to the x axis. Using Fermat's Principle, derive the equation of the relecting surface.

I am doing this on my palm pilot right now, so I will try to draw a picture of my thoughts.
 

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Anyone? Am I on the right track?
 
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