Question

The parabola with focus (0, 5) and directrix y = -5.

Answer 1

What is the question?

Answer 2

well actually I just need help with figuring out this equation

Answer 3

since the focus is at (0,5) and the directrix is at \(y=-5\) you know this parabola opens up and has vertex at the origin (0,0)

Answer 4

therefore the equation looks like \(4py=x^2\) and since \(p=5\) you get \(20y=x^2\)

Answer 5

@aussy123 do you have any question?

Answer 6

where did you get the 4

Answer 7

From parabola formula ( x -h)² = 4p ( y - k)

Answer 8

That's the parabola rule to memorize!

Answer 9

oh i was givin the distance formula but thanks ill write this formula down

Answer 10

i got it directly from the old school way to write a parabola with vertex \((h,k)\)
it is either \((y-k)^2=4p(x-h)\) or \((x-h)^2=4p(y-k)\) depending on how it opens, to the right/left or up/down

Answer 11

in your case it opens up, and the vertex is at (0,0) so i wrote \(4py=x^2\)

Answer 12

oh ok that nakes alot of sense thx

Answer 13

then since \(p=5\) is the focus, we know it is \(4\times 5y=x^2\)