Designing a Mirror by Quad. Eq

I think you are talking about Parabolic Reflector.
Please refer to the follow website:
http://en.wikipedia.org/wiki/Parabolic_reflector
The quadratic equation of the parabolic mirror described in the website is:
x^2 = 4ay, where F(0,a) is the focus of the parabola and V is the origin.

2009-06-17 19:53:08 補充：
That's good. You will find more information on Parabolic Mirror, the quadratic equation involved and the proof of the property that the tangent to parabola at a point bisects the angle between the segments joining the point to the focus and the directrix.
Please refer to the follow website:
http://en.wikipedia.org/wiki/Parabolic_reflector
The quadratic equation of the parabolic mirror described in the website is:
x^2 = 4ay, where F(0,a) is the focus of the parabola and V is the origin.
When the light beam moving vertically downwards in the concavity of the parabola will bounce off the parabola and moving directly towards the focus.

More information on Parabolic Mirror :
http://www.cut-the-knot.org/Curriculum/Geometry/ParabolaMirror.shtml

The proof is quite lengthy and it is difficult for me to draw the figure here.
However, you can find the proof in the following website using Java and it is interactive.
You have to select all items including names, focus, axes, directrix, tangent and statement:
http://www.cut-the-knot.org/Curriculum/Geometry/ParabolaFocal.shtml

I hope this can help you to design your Parabolic Mirror.

What objectives have to achieve in designing the mirror?