The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$y ^ { 2 } = 12 x$$
A) focus: $( 3,0 )$
directrix: $x = - 3$
B) focus: $( 0,3 )$
directrix: $y = - 3$
C) focus: $( 3,0 )$
directrix: $x = 3$
D) focus: $( 0 , - 3 )$
directrix: $y = - 3$

Question

Quizplus · Accepted Answer

The given equation $y^2 = 12x$ is a parabola that opens to the right with its vertex at the origin (0,0). The standard form of a parabola opening to the right or left is $y^2 = 4px$, where $p$ is the distance from the vertex to the focus and also from the vertex to the directrix. Here, $4p = 12$, so $p = 3$. Therefore, the focus is at $(3,0)$, and the directrix is the line $x = -3$.

The Parabola 1 Graph Parabolas with Vertices at the Origin y2=12xy ^ { 2 } = 12 xy2=12x

The Parabola
1 Graph Parabolas with Vertices at the Origin $y ^ { 2 } = 12 x$