What is the equation in standard form of the parabola with a focus at (0,0) and a directrix of y= 4?

1 Answer
Nallasivam V
Dec 30, 2017

#y=- x^2/8 + 2#

Explanation:

Given -
Focus #(0,0)#
Directrix #y=4#

It vertex lies at equidistance between focus and directrix.

So, vertex #(0, 2)#

The directrix is parallel to the y-axis.
The parabola opens downward.

The general form of the equation is -

#(x-h)^2=-4a(y-k)#
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Where #(h, k)# are the coordinates of the vertex
#a# is the distance of the vertex from focus.

#(x-0)^2=-4xx2xx(y-2)#

#x^2=-8y+16#

#-8y+16=x^2#
#-8y=x^2-16#
#y=- x^2/8 + 2#

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