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Mamont248 [21]
3 years ago
7

What equation represents a parabola with a focus of (0,4) and a directrix of y=2

Mathematics
1 answer:
scZoUnD [109]3 years ago
7 0
We know that

Any point <span>(x,y)</span> on the parabola is equidistant from the focus and the directrix

Therefore,

focus (0,4) and directrix of y=2

<span>√[<span>(x−0)</span></span>²+(y−4)²]=y−(2)

<span>√[x</span>²+(y-4)²]=y-2

x²+(y-4)²=(y-2)²

x²+y²-8y+16=y²-4y+4

x²=4y-12-----> 4y=x²+12----->y= (x²/4)+3


the answer is

y= (x²/4)+3


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