Find the equation in standard form of the parabola described.
-The vertex has coordinates (3, -5), and the focus has coordinates (4, -5).
A) $( x + 3 ) ^ { 2 } = 4 ( y - 5 )$
B) $( y + 5 ) ^ { 2 } = - 4 ( x - 3 )$
C) $( y + 5 ) ^ { 2 } = 4 ( x - 3 )$
D) $( x + 3 ) ^ { 2 } = - 4 ( y - 5 )$

Question

Find the equation in standard form of the parabola described.
-The vertex has coordinates (3, -5), and the focus has coordinates (4, -5). 
A) $( x + 3 ) ^ { 2 } = 4 ( y - 5 )$
B) $( y + 5 ) ^ { 2 } = - 4 ( x - 3 )$
C) $( y + 5 ) ^ { 2 } = 4 ( x - 3 )$
D) $( x + 3 ) ^ { 2 } = - 4 ( y - 5 )$

Quizplus · Accepted Answer

The correct equation is $( y + 5 ) ^ { 2 } = 4 ( x - 3 )$. This is because 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 focus. Here, the vertex is (3, -5) and the focus is (4, -5), indicating a horizontal opening with p=1.

Find the Equation in Standard Form of the Parabola Described (x+3)2=4(y−5)( x + 3 ) ^ { 2 } = 4 ( y - 5 )(x+3)2=4(y−5)

Find the Equation in Standard Form of the Parabola Described $( x + 3 ) ^ { 2 } = 4 ( y - 5 )$