What is the equation of the quadratic graph with a focus of (3, 4) and a directrix of y = 8? (1 point)

equation become (x -3)² =  -8(y - 6).

Step-by-step explanation:

Given  :  focus of (3, 4) and a directrix of y = 8.

To find : What is the equation of the quadratic graph.

Solution : We have given

Focus = (3, 4).

directrix  y = 8.

The standard form is (x - h)² = 4p (y - k),

where the focus is (h, k + p) and the directrix is y = k - p.

On comparing

(h, k + p) =  (3, 4).

h = 3 ,

From focus

k + p = 4 (1)

From directrix

y = k -p

k -p = 8 (2)

Adding both the equation 1 and 2

k + p = 4 (1)

k -p = 8 (2).

2k = 12 .

On dividing by 2

k = 6.

Plug k =6 in equation 1

k + p = 4

6 + p = 4

P = -2 .

Plug all the values in standard equation :

(x - h)² = 4p (y - k),

(x - 3)² = 4(-2) (y - 6).

(x -3)² =  -8(y - 6).

Therefore, equation become (x -3)² =  -8(y - 6).