How do you find the equation of the parabola whose Focus (0,-1/4) and directrix (0,1/4)?

1 Answer
BeeFree
Nov 29, 2015

The vertex will lie halfway between the focus and directrix.

Explanation:

I think you meant to write that the directrix is #y=1/4#. Assuming that is true, then the directrix lies above the focus, so this parabola opens downward (concave down).

Vertex #=(0,0)# which is halfway between the focus and directrix.

Distance between focus and vertex #p= 1/4#

Coefficient #abs(a)=1/(4xx1/4)=1#

The sign on #a# is negative , so #a=-1#

Equation of parabola : #y=-x^2#

hope that helps!

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