What is the vertex, directrix, and focus of this porabola?

Question

(X+2)^2=8y-24

Answer 1

Given parabola equation : (x+2)² = 8y - 24

8y = ( x - (-2) )² + 24

y = (1/8)( x - (-2) )² + 24/8

y = (1/8)( x - (-2) )² + 3

Compare equation with standard from of parabola [ y = a( x - h )² + k ] and write the coefficients.

a = 1/8 , h = - 2 , k = 3

Vertex : (h , k ) = ( - 2 , 3 )

Directrix = directed distance from vertex to focus p = 1/(4a) = 1/(4(1/8)) = 8/4 = 2

Focus : (h, k + p) = (- 2 , 3+2) = (- 2 , 5 )

Solution : vertex : ( - 2 , 3 ) , Directrix : p = 2  and  Focus : (- 2 , 5 ).