Write the standard form of the equation of the parabola with focus (-5,5) and its vertex at (-5,8) .
A) $( y - 8 ) ^ { 2 } = - 3 ( x + 5 )$
B) $( y - 8 ) ^ { 2 } = 12 ( x + 5 )$
C) $( x + 5 ) ^ { 2 } = - 12 ( y - 8 )$
D) $( x + 5 ) ^ { 2 } = - 3 ( y - 8 )$
E) $( y - 8 ) ^ { 2 } = - 12 ( x + 5 )$

Question

Quizplus · Accepted Answer

The parabola opens downwards because the focus is below the vertex. The standard form of a parabola opening vertically is $(x - h)^2 = 4p(y - k)$, where (h, k) is the vertex and p is the distance from the vertex to the focus. Here, $h = -5$, $k = 8$, and $p = -3$ (since the focus is 3 units below the vertex). Substituting these values gives $(x + 5)^2 = -12(y - 8)$.

Write the Standard Form of the Equation of the Parabola (y−8)2=−3(x+5)( y - 8 ) ^ { 2 } = - 3 ( x + 5 )(y−8)2=−3(x+5)

Write the Standard Form of the Equation of the Parabola $( y - 8 ) ^ { 2 } = - 3 ( x + 5 )$