Find the focus, directrix, and focal diameter of the parabola.

Question

y2 = 8x

Answer 1

This is an X-parabola.

Y^2 = 8x.
X = (1/8)y^2

k = Yv = -b/2a = 0/(1/4) = 0
h = Xv = (1/8*0^2 = 0.
V(h,k) = V(0,0).

D(X1,K), V(h,k), F(X2,K).
D(X1,0), V(0,0), F(X2,0).

DV = 0-X1 = 1/4a.
0-X1 = 1/(1/2) = 2.
X1 = -2.

VF = X2-0 = 1/4a
X2 = 1/(1/2) = 2

Focal Dia.(Ver. line).
A(2,Y1), F(2,0), B(2,Y2).

a = 1/8
1/a = 8 = Focal Dia.

AF = 0-Y1 = 8/2 = 4.
Y1 = -4.

FB = Y2-0 = 8/2 = 4
Y2 = 4.