Find the vertex and focus of the parabola below.
$$y ^ { 2 } + 10 y - 8 x + 30 = 0$$
A) Vertex: $\left( - \frac { 5 } { 8 } , 5 \right)$
Focus: $\left( \frac { 11 } { 8 } , 5 \right)$
B) Vertex: $\left( \frac { 5 } { 8 } , - 5 \right)$
Focus: $\left( \frac { 21 } { 8 } , - 5 \right)$
C) Vertex: $\left( \frac { 5 } { 8 } , - 5 \right)$
Focus: $\left( \frac { 69 } { 8 } , - 5 \right)$
D) Vertex: $\left( - \frac { 5 } { 8 } , 5 \right)$
Focus: $\left( \frac { 59 } { 8 } , 5 \right)$
E) Vertex: $\left( - \frac { 5 } { 8 } , - 5 \right)$
Focus: $\left( \frac { 59 } { 8 } , - 5 \right)$

Question

Quizplus · Accepted Answer

The given equation can be rewritten in the form $(y + 5)^2 = 8(x + \frac{5}{8})$, indicating a parabola that opens to the right. The vertex is $\left( \frac{5}{8}, -5 \right)$ and the focus is $\left( \frac{21}{8}, -5 \right)$.

Find the Vertex and Focus of the Parabola Below y2+10y−8x+30=0y ^ { 2 } + 10 y - 8 x + 30 = 0y2+10y−8x+30=0

Find the Vertex and Focus of the Parabola Below $y ^ { 2 } + 10 y - 8 x + 30 = 0$