Find the vertex, focus, and directrix of the parabola $x ^ { 2 } = 7 y$
A) $V ( 0,7 ) , F ( 0,7 ) , x = - 7$
B) $V ( 7,0 ) , F \left( \frac { 7 } { 4 } , 0 \right) , y = \frac { 7 } { 4 }$
C) $V ( 0,0 ) , F \left( 0 , - \frac { 7 } { 4 } \right) , x = \frac { 7 } { 4 }$
D) $V ( 0,0 ) , F \left( 0 , \frac { 7 } { 4 } \right) , y = - \frac { 7 } { 4 }$
E) $V \left( 0 , \frac { 7 } { 4 } \right) , F \left( 0 , \frac { 7 } { 4 } \right) , y = - \frac { 7 } { 4 }$

Question

Quizplus · Accepted Answer

The equation $x^2 = 7y$ is in the form $x^2 = 4py$, indicating a parabola that opens upwards with its vertex at the origin $(0,0)$. The value of $4p = 7$, so $p = \frac{7}{4}$. The focus, therefore, is $(0, p)$ or $\left(0, \frac{7}{4}\right)$, and the directrix is $y = -p$ or $y = -\frac{7}{4}$.

Find the Vertex, Focus, and Directrix of the Parabola x2=7yx ^ { 2 } = 7 yx2=7y

Find the Vertex, Focus, and Directrix of the Parabola $x ^ { 2 } = 7 y$