What is the equation of the parabola with a focus at (3,18) and a directrix of y= 17?

1 Answer
Binayaka C.
Jun 5, 2017

The equation of parabola is #y=1/2(x-3)^2+17.5#

Explanation:

The focus is at #(3,18)# .Directrix is #y=17#

The vertex is at equidistant from focus and directrix. So vertex is at #(3,17.5)#. Distance of directrix from vertex is #d=0.5:. a= 1/(4d)=1/(4*1/2)=1/2#

The standard equation of parabola is #y=a(x-h)^2+k ; (h,k)# being vertex. Here the directrix is behind vertex, so parabola opens upward and #a# is positive.

So the equation of parabola is #y=1/2(x-3)^2+17.5 #
graph{1/2(x-3)^2+17.5 [-80, 80, -40, 40]} [Ans]

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