Question

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 9).

Answer 1

@ganeshie8

Answer 2

HI!!

Answer 3

For the parabola above,
the equation is
y=x^2/(4p)
where p=distance from vertex to focus=distance from vertex to directrix.
Since you know the vertex (0,0), and the focus (0,9), you should be able to find p, and hence the equation of the parabola.

Answer 4

do you know what it looks like? if so, this takes one second

Answer 5

p = 9

Answer 6

yes of course

Answer 7

making this
\[36y=x^2\]

Answer 8

Would that be equal to y = \(\dfrac1{36}x^2\)?

Answer 9

Or \(y = \dfrac{1}{36}x^2\)

Answer 10

@misty1212

Answer 11

they are the same right?

Answer 12

usually it is
\[4p(y-k)=(x-h)^2\] as a standard form

Answer 13

but \[36y=x^2\] is the same as \[y=\frac{1}{36}x^2\]

Answer 14

Thank you so much! :)