What is the vertex form of the equation of the parabola with a focus at (2,-13) and a directrix of #y=23 #?

1 Answer
Binayaka C.
Jun 28, 2016

The equation of parabola is #y=-1/72(x-2)^2+5#

Explanation:

The vertex is at midway between focus#(2,-13)#and directrix #y=23 :.#The vertex is at #2,5# The parabola opens down and the equation is #y= -a(x-2)^2+5# The vertex is at equidistance from focus and vertex and the distance is #d=23-5=18# we know #|a|=1/(4*d) :.a=1/(4*18)=1/72#Hence the equation of parabola is #y=-1/72(x-2)^2+5# graph{-1/72(x-2)^2+5 [-80, 80, -40, 40]}[Ans]

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