Determine the standard form of an equation of the parabola subject to the given conditions.
-Vertex: $( - 1 , - 3 )$; Directrix: $x = - 5$
A) $( y + 3 ) ^ { 2 } = 16 ( x + 1 )$
B) $( x + 1 ) ^ { 2 } = 16 ( y + 3 )$
C) $( y + 3 ) ^ { 2 } = - 5 ( x + 1 )$
D) $( x + 1 ) ^ { 2 } = - 5 ( y + 3 )$

Question

Quizplus · Accepted Answer

The vertex form of a parabola that opens horizontally is $(y-k)^2=4p(x-h)$, where $(h,k)$ is the vertex and $p$ is the distance from the vertex to the directrix. Here, the vertex is $(-1,-3)$ and the directrix is $x=-5$, indicating the parabola opens to the right (since the directrix is to the left of the vertex) and $p=4$. Substituting $h=-1$, $k=-3$, and $p=4$ into the formula gives $(y+3)^2=16(x+1)$.

Determine the Standard Form of an Equation of the Parabola (−1,−3)( - 1 , - 3 )(−1,−3)

Determine the Standard Form of an Equation of the Parabola $( - 1 , - 3 )$