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# what is the equation of the parabola whose focus is (-3,1) and directrix is Y=4?

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what is the equation of the parabola whose focus is (-3,1) and directrix is Y=4?

Guest May 21, 2017
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Because the directrix is a horizontal line, the parabola will be vertical.

Because the focus is below the directrix, the parabola will open downward.

The vertex of the parabola will be half-way between the focus and the directrix:  vertex  =  (-3, 2.5)

The focal length is the distance from the focus to the vertex:  focal length is:  f = 1.5

An equation for a parabola is:  y - y1 =  a(x - x1)

with a being found be the formula:  a  =  1/(4f)     --->     a  =  1/(4ยท1.5)     --->     a  =  1/6

and (x1, y1) being the vertex     --->     x1  =  -3     and     y1  =  2.5.

Therefore, an equation is:  y - 2.5  =  (1/6)(x + 3)

geno3141  May 21, 2017

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