The directrix of a parabola is y=9 . The focus of the parabola is (2,5) .

What is the equation of the parabola?

y=−1/8(x−2)^2+7

y=1/8(x−2)^2−7

y=1/8(x−2)^2+7

y=−1/8(x−2)^2−7

6 answers

same as
https://www.jiskha.com/questions/1815358/the-directrix-of-a-parabola-is-y-4-the-focus-of-the-parabola-is-2-2-what-is
They are different questions.
geeesssh, I know that
The method is the same!
I don't understand it well.
1. Look for examples in your book
2. Follow method used in class.
3. Explain to your teacher what part you don't understand.
The parabola x^2 = 4py has
focus = (0,p)
directrix y = -p
The distance between focus and directrix is 2p
For your parabola, that distance is 5-9 = -4 = 2p, so the usual equation would be
x^2 = -8y

But the focus is at (2,5) and not (0,-2). So it has been shifted right 2 and up 7. That makes the equation
(x-2)^2 = -8(y-7)
So pick the choice that matches.
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