Find the vertex and focus of the parabola.

Question

(x^2)-(24y) = 0

Answer 1

X^2 - 24Y = 0.

24Y = X^2,
Y = X^2 / 24,
Y = 1/24 (X^2).

Vertex Form: Y = a(x - h)^2 + k.
h = 0, k = 0. a = 1/24.
V(h , k) = V(0 , 0).

The distance from vertex to focus point = 1/4a.

F(0 , Yf),
Yf - k = 1/4a,
Yf - 0 = 1/4a,
Yf = 1/4a.

4a = 4 * 1/24 = 4/24 = 1/6.
Yf = 1/4A = 6/1 = 6.

F(h , Yf) = F(0 , 6).

Answer 2

Nice one