Directrix is a horizontal line, so the parabola is of the form
(x-h)^2= 4p(y-k) , where (h,k) is the vertex
Coordinates of the focus is (h, k+p)
h = 8 (same as the focus)
k+p = -8 -----(1)
equation of directrix is y=k-p
k-p = -6 ------(2)
from (1) & (2)
2k = -14
k=-7
-7+p= -8
p = -1
vertex = (8,-7)
(x-8)^2 = -4(y+7)
y+7 = (-1/4) (x-8)^2
y = (-1/4)(x-8)^2 - 7 is the parabola
What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1?
Directrix is a horizontal line, so the parabola is of the form
(x-h)^2= 4p(y-k) , where (h,k) is the vertex
Coordinates of the focus is (h, k+p)
h = 1 (same as the focus)
k+p = 1 -----(1)
equation of directrix is y=k-p
k-p = -1 ------(2)
from (1) & (2)
2k = 0
k=0
0+p= 1
p = 1
vertex = (1,0)
(x-1)^2 = 4(y-0)
(x-1)^2=4y
y = (1/4) (x-1)^2 is the parabola
