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magentarita · #3 October 16th, 2008, 08:03 PM

Quote:

Originally Posted by earboth

I assume that the paraboloid has an opening of 4'' and a depth of 3''. If so:

The cross-section of the paraboloid through the focus and the vertex of the paraboloid must be a parabola. Use a coordinate system where the vertex is V(0, 0) and the point P(3, 2) are located on the parabola.

The general equation of a parabola opening to the right is:

$y^2 = 2p\cdot x$

Use the coordinates of P to calculate p. (I've got $p = \frac23$ )

Then the focus F is the point where all parallel light rays will be concentrated. F has the coordinates $F\left(\frac p2\ ,\ 0\right)$

Another great and helpful reply.