Answer:
equation become (x -3)² = -8(y - 6).
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).