Find the vertex and focus of the parabola. $$y ^ { 2 } = \frac { 7 } { 9 } x$$
A) vertex: $( 0,0 )$ focus: $\left( 0 , \frac { 7 } { 9 } \right)$
B) vertex: $( 0,0 )$ focus: $\left( \frac { 7 } { 9 } , 0 \right)$
C) vertex: $( 0,0 )$ focus: $\left( \frac { 7 } { 36 } , 0 \right)$
D) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( \frac { 7 } { 9 } , \frac { 7 } { 9 } \right)$
E) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , \frac { 7 } { 36 } \right)$

Question

Find the vertex and focus of the parabola. $$y ^ { 2 } = \frac { 7 } { 9 } x$$ 
A) vertex: $( 0,0 )$ focus: $\left( 0 , \frac { 7 } { 9 } \right)$
B) vertex: $( 0,0 )$ focus: $\left( \frac { 7 } { 9 } , 0 \right)$
C) vertex: $( 0,0 )$ focus: $\left( \frac { 7 } { 36 } , 0 \right)$
D) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( \frac { 7 } { 9 } , \frac { 7 } { 9 } \right)$
E) vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , \frac { 7 } { 36 } \right)$

Quizplus · Accepted Answer

The given equation is in the form $y^2 = 4px$, where $4p = \frac{7}{9}$, so $p = \frac{7}{36}$. The vertex of a parabola in this form is at the origin $(0,0)$, and the focus, being $p$ units away from the vertex in the direction of the parabola's opening (which is to the right since $x$ is positive), is at $\left(\frac{7}{36}, 0\right)$.

Find the Vertex and Focus of the Parabola y2=79xy ^ { 2 } = \frac { 7 } { 9 } xy2=97​x

Find the Vertex and Focus of the Parabola $y ^ { 2 } = \frac { 7 } { 9 } x$