Find an equation of the parabola that satisfies the condition. Vertex $V ( - 4,0 )$ , focus $F ( - 2,0 )$
A) $y = 8 ( x + 4 ) ^ { 2 }$
B) $y ^ { 2 } = 8 ( x - 4 )$
C) $y ^ { 2 } = 8 ( x + 4 )$
D) $y ^ { 2 } = ( x + 4 )$
E) $x ^ { 2 } = 8 ( y + 4 )$

Question

Quizplus · Accepted Answer

The distance from the vertex to the focus is 2, so the distance from the vertex to the directrix is also 2. The equation of the parabola is of the form $y^2=4p(x-h)$, where $h$ is the x-coordinate of the vertex and $p$ is the distance from the vertex to the directrix. Substituting the given values, we get $y^2=4(2)(x+4)$, which simplifies to $y^2=8(x+4)$.

Find an Equation of the Parabola That Satisfies the Condition V(−4,0)V ( - 4,0 )V(−4,0)

Find an Equation of the Parabola That Satisfies the Condition $V ( - 4,0 )$