What is the standard form of the equation of the parabola with a directrix at x=3 and a focus at (-5,-5)?

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Answer 1 · 2018-06-02T11:27:40

The equation of parabola is $(y+5)^2 = -16(x+1)$

Focus is at $(-5,-5)$ and directrix is $x=3$ . Vertex is at midway

between focus and directrix. Therefore vertex is at

$((-5+3)/2,-5) or (-1,-5)$ The directrix is at the right side

of vertex ,so, the horizontal parabola opens left. The equation of

horizontal parabola opening left is $(y-k)^2 = -4 p(x-h)$

$h=-1 ,k=-5$ or $(y+5)^2 = -4 p(x+1)$ . the distance

between focus and vertex is $p=5-1=4$ . Thus the standard

equation of horizontal parabola is $(y+5)^2 = -4*4(x+1)$

or $(y+5)^2 = -16(x+1)$

graph{(y+5)^2= -16(x+1) [-80, 80, -40, 40]} [Ans]