What is the standard form of the equation of the parabola with a directrix at x=-3 and a focus at (6,2)?

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Answer 1 · 2017-12-31T11:56:57

The standard equation of horizontal parabola is
$(y-2)^2 = 18(x-1.5)$

Focus is at $(6,2)$ and directrix is $x=-3$ . Vertex is at midway

between focus and directrix. Therefore vertex is at

$((6-3)/2,2) or (1.5,2)$ .Here the directrix is at left of

the vertex , so parabola opens right and $p$ is positive.

The standard equation of horizontal parabola opening right is

$(y-k)^2 = 4p(x-h) ; h=1.5 ,k=2$

or $(y-2)^2 = 4p(x-1.5)$ The distance between focus and

vertex is $p=6-1.5=4.5$ . Thus the standard equation of

horizontal parabola is $(y-2)^2 = 4*4.5(x-1.5)$ or

$(y-2)^2 = 18(x-1.5)$

graph{(y-2)^2=18(x-1.5) [-40, 40, -20, 20]}