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

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

C) vertex: $( 2,3 )$
focus: $( 2,8 )$
$\text { directrix: } x=-2$

D) vertex: $( 3,2 )$
focus: $( 3 , - 3 )$
$\text { directrix: } y=7$

directrix: $y = 8 \quad$ directrix: $y = 2 \quad$ directrix: $x = - 2 \quad$ 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: $( 2 , - 2 )$
$\text { directrix: } y=8$

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

C) vertex: $( 2,3 )$
focus: $( 2,8 )$
$\text { directrix: } x=-2$

D) vertex: $( 3,2 )$
focus: $( 3 , - 3 )$
$\text { directrix: } y=7$

directrix: $y = 8 \quad$ directrix: $y = 2 \quad$ directrix: $x = - 2 \quad$ directrix: $y = 7$

Quizplus · Accepted Answer

The given equation is in the form $(x - h)^2 = 4p(y - k)$, where $(h, k)$ is the vertex. Here, $h = 2$ and $k = 3$, so the vertex is $(2, 3)$. Since $4p = -20$, $p = -5$, indicating the parabola opens downwards. The focus is $p$ units below the vertex, so it's $(2, 3 - 5) = (2, -2)$. The directrix is a horizontal line $p$ units above the vertex, so it's $y = 3 + 5 = 8$.

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