The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$x ^ { 2 } = 8 y$$
A) focus: $( 0,2 )$
directrix: $y = - 2$
B) focus: $( 2,0 )$
directrix: $y = 2$
C) focus: $( 2,0 )$
directrix: $x = 2$
D) focus: $( 0 , - 2 )$
directrix: $x = - 2$

Question

Quizplus · Accepted Answer

The equation $x^2 = 8y$ represents a parabola opening upwards with its vertex at the origin (0,0). The focus is at $(0, \frac{1}{4}a)$ and the directrix is $y = -\frac{1}{4}a$, where $4a = 8$, so $a = 2$. Therefore, the focus is at $(0,2)$ and the directrix is $y = -2$.

The Parabola 1 Graph Parabolas with Vertices at the Origin x2=8yx ^ { 2 } = 8 yx2=8y

The Parabola
1 Graph Parabolas with Vertices at the Origin $x ^ { 2 } = 8 y$