Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.

Standard form (x - 0)² = 4(-9) (y - 0).

Step-by-step 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).

so, converting firstly the mixed fractions to improper fractions and then "adding".

hope this is what you were asking for!

step-by-step explanation: