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scoray [572]
2 years ago
11

Find the standard form of the equation of the parabola with a focus at (0, 5) and a directrix at y = -5.

Mathematics
1 answer:
bekas [8.4K]2 years ago
5 0
The focus-directrix form of a parabola is (x - h)²<span> = 4p (y - k), where the </span>focus<span> is (h, k + p) and the directrix is y = k - p.
in this case,
h=0
k+p=5
k-p=-5
solve for p and k: (k+p)+(k-p)=5+(-5), 2k=0, k=0, p=5
</span>(x-0)²=4*5(y-0), x²=20y<span>
so the standard form of a parabola is y=ax</span>²+bx+c
<span>in this case, it is :y=(1/20)x</span>²
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