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

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

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Answer 1 · 2015-11-29T01:29:20

The vertex will lie halfway between the focus and directrix.

Explanation:

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

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

Distance between focus and vertex $p = \frac{1}{4}$ $p= 1/4$

Coefficient $| a | = \frac{1}{4 \times \frac{1}{4}} = 1$ $abs(a)=1/(4xx1/4)=1$

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

Equation of parabola : $y = - x^{2}$ $y=-x^2$

hope that helps!

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

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