What is the equation of the parabola with a focus at (15,19) and a directrix of y= 20?

1 Answer
Nov 24, 2015

The directrix is above the focus, so this is a downward opening parabola.


The vertex will lie exactly halfway between the directrix and the focus:


The distance #p# between the vertex and the focus is #p=1/2#, so the absolute value of the coefficient #abs(a) = 1/(4p)= 1/2# Now, since we know the parabola opens downward, the sign on the coefficient must be negative.

Here is the final equation:


hope that helped

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