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kobusy [5.1K]
3 years ago
7

A parabola has a focus of F(−2,6) and a directrix of x=6. The point P(x,y) represents any point on the parabola, while D(6,y), r

epresents any point on the directrix. What is the equation for this parabola?
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
8 0
Equation of a parabola: (x - h)²<span> = 4p (y - k), where the </span>focus<span> is (h, k + p) and the </span>directrix<span> is y = k - p
in this case, the directric is x=6, so the parabola opens sideways, the equation becomes </span>(y<span> - </span>k)²<span> = 4p (</span>x<span> - </span>h<span>), where the </span>focus is (h<span> + </span>p<span>, </span>k) and the directrix is x<span> = </span>h<span> - </span>p<span>. 
</span>h-p=6
h+p=-2
solve: h=2, p=-4
k=6
plug in the h, p, and k values, so the equation is (y-6)²=-16(x-2)
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