Find the vertex and focus of the parabola.
$$x ^ { 2 } - 8 y = 0$$
A) vertex: $( 2,0 ) \quad$ focus: $( 0,0 )$
B) vertex: $( - 2,0 )$ focus: $( 0,0 )$
C) vertex: $( 0,0 ) \quad$ focus: $( 2,0 )$
D) vertex: $( 0,0 ) \quad$ focus: $( 0,2 )$
E) vertex: $( 0,0 ) \quad$ focus: $( 0 , - 2 )$

Question

Quizplus · Accepted Answer

The given equation $x^2 - 8y = 0$ can be rewritten as $x^2 = 8y$, which is a parabola opening upwards with its vertex at the origin $(0,0)$. The standard form of a parabola opening upwards is $x^2 = 4py$, where $p$ is the distance from the vertex to the focus. Comparing $4p = 8$ gives $p = 2$, so the focus is $(0,2)$.

Find the Vertex and Focus of the Parabola x2−8y=0x ^ { 2 } - 8 y = 0x2−8y=0

Find the Vertex and Focus of the Parabola $x ^ { 2 } - 8 y = 0$