Answer:
Standard form (x - 0)² = 4(-9) (y - 0).
Explanation:
Given : parabola with a focus at (0, -9) and a directrix y = 9.
To find : Find the standard form of the equation .
Solution : We have given focus at (0, -9) and a directrix y = 9.
Standard form of the equation: (x - h)² = 4p (y - k).
Where the focus is (h, k + p) and the directrix is y = k - p.
Focus ( h , k+p ) = ( 0 , -9) ;
Here , h = 0 ,
k + p = -9 .
directrix y = 9.
k - p = 9
k + p = -9
___________ ( On adding )
2k = 0
k = 0.
Then k - p = 9
Plug k = 0
0 - p = 9
p = - 9.
Plug all values in standard form of parabola.
(x - 0)² = 4(-9) (y - 0).
Therefore, Standard form (x - 0)² = 4(-9) (y - 0).