for the equation -4x-8y^2=0,give the focus and directrix.then sketch the graph, showing both the focus and the directrix. please show all the step thank you.

Answer 1

-4x-8y^2 = 0
-4x = 8y^2
X = -2y^2
This is an X-parabola; it opens to the left because "a" is negative.

K = -b/2a = 0/-4 = 0
h = 0^2 = 0
V(h,K) = V(0,0).

D(X1,0), V(0,0), F(X2,0).

X1 = h - |1/4a| = 0 - 1/8 = -1/8.

X2 = h + |1/4a| = 0 + 1/8 = 1/8.

Use the following points for graphing:

(X,Y)
(-8,-2)
(-2,-1)
V(0,0)
(-2,1)
(-8,2)

Answer 2

CORRECTION:

F(X1,0), V(0,0), D(X2,0).