Find the vertex, focus, and directrix of the parabola with the given equation.
-$$( y + 1 ) ^ { 2 } = 16 ( x + 3 )$$
A) vertex: $( - 3 , - 1 )$
focus: $( - 7 , - 1 )$
directrix: $x = 1$

B) vertex: $( - 1 , - 3 )$
focus: $( 3 , - 3 )$
directrix: $x = - 5 \quad$

C) vertex: $( - 3 , - 1 )$
focus: $( 1 , - 1 )$
directrix: $x = - 7$

D) vertex: $( 3,1 )$
focus: $( 7,1 )$
directrix: $x = - 1$

Question

Find the vertex, focus, and directrix of the parabola with the given equation.
-$$( y + 1 ) ^ { 2 } = 16 ( x + 3 )$$
A) vertex: $( - 3 , - 1 )$
focus: $( - 7 , - 1 )$
directrix: $x = 1$

B) vertex: $( - 1 , - 3 )$
focus: $( 3 , - 3 )$
directrix: $x = - 5 \quad$

C) vertex: $( - 3 , - 1 )$
focus: $( 1 , - 1 )$
directrix: $x = - 7$

D) vertex: $( 3,1 )$
focus: $( 7,1 )$
directrix: $x = - 1$

Quizplus · Accepted Answer

The given equation $( y + 1 ) ^ { 2 } = 16 ( x + 3 )$ is in the form $(y-k)^2 = 4p(x-h)$, where the vertex is $(h, k)$. Here, $h = -3$ and $k = -1$, so the vertex is $(-3, -1)$. The value of $4p = 16$ gives $p = 4$. Since the parabola opens to the right, the focus is $(h+p, k) = (-3+4, -1) = (1, -1)$, and the directrix is $x = h-p = -3-4 = -7$.

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