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
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
They are different questions.
geeesssh, I know that
The method is the same!
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.
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.
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.
2 answers