Find the vertex, focus, and directrix of the parabola with the given equation.
-$( x - 2 ) ^ { 2 } = - 20 ( y - 3 )$
A) vertex: $ (2,3) $
focus: $ (2,-2) $
directrix: $ y=8 $

B) vertex: $ (-2,-3) $
focus: $ (-2,-8) $
directrix: $ \mathrm{y}=2 $

C) vertex: $ (2,3) $
focus: $ (2,8) $
directrix: $ x=-2 $

D) vertex: $ (3,2) $
focus: $ (3,-3) $
directrix: $ y=7 $

Question

Find the vertex, focus, and directrix of the parabola with the given equation.
-$( x - 2 ) ^ { 2 } = - 20 ( y - 3 )$
A) vertex: $ (2,3) $
focus: $ (2,-2) $
directrix: $ y=8 $

B) vertex: $ (-2,-3) $
focus: $ (-2,-8) $
directrix: $ \mathrm{y}=2 $

C) vertex: $ (2,3) $
focus: $ (2,8) $
directrix: $ x=-2 $

D) vertex: $ (3,2) $
focus: $ (3,-3) $
directrix: $ y=7 $

Quizplus · Accepted Answer

The given equation is in the form $(x - h)^2 = 4p(y - k)$, where the vertex is $(h, k) = (2, 3)$. Since $4p = -20$, $p = -5$, indicating the focus is 5 units below the vertex, at $(2, 3-5) = (2, -2)$, and the directrix is $y = k + p = 3 + 5 = 8$.

Find the Vertex, Focus, and Directrix of the Parabola with the Given