Question

What is the equation of the quadratic graph with a focus of (8, −8) and a directrix of y = −6? (1 point)

Answer 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 = 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