What is the equation of the parabola with a focus at (34,22) and a directrix of y= 32?

1 Answer
Sep 27, 2016

Equation of the parabola is #y= -1/40(x-34)^2+22#

Explanation:

The equation of the parabola with vertex at#(34,22)# is #y=a(x-34)^2+22# The directrix of #y=32# is behind the vertex. So The distance of directrix from vertex is #d=32-22=10#. The parabola opens down, so #a# is negative. We know #a=1/(4d)=1/40#
Hence equation of the parabola is #y= -1/40(x-34)^2+22# graph{-1/40(x-34)^2+22 [-160, 160, -80, 80]}[Ans]