Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
-$$x = 6 y ^ { 2 }$$
A) focus: $\left( \frac { 1 } { 24 } , 0 \right)$
directrix: $x = - \frac { 1 } { 24 }$
B) focus: $\left( 0 , \frac { 1 } { 24 } \right)$
directrix: $\mathrm { y } = - \frac { 1 } { 24 }$
C) focus: $\left( \frac { 1 } { 6 } , 0 \right)$
directrix: $x = - \frac { 1 } { 6 }$
D) focus: $\left( \frac { 1 } { 24 } , 0 \right)$
directrix: $x = \frac { 1 } { 24 }$

Question

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
-$$x = 6 y ^ { 2 }$$
A) focus: $\left( \frac { 1 } { 24 } , 0 \right)$
directrix: $x = - \frac { 1 } { 24 }$
B) focus: $\left( 0 , \frac { 1 } { 24 } \right)$
 directrix: $\mathrm { y } = - \frac { 1 } { 24 }$ 
C) focus: $\left( \frac { 1 } { 6 } , 0 \right)$
directrix: $x = - \frac { 1 } { 6 }$
D) focus: $\left( \frac { 1 } { 24 } , 0 \right)$
 directrix: $x = \frac { 1 } { 24 }$

Quizplus · Accepted Answer

The vertex of the parabola is at the origin, which means the equation is of the form $x=4py$, where $p$ is the distance from the vertex to the focus and directrix. Comparing this with the given equation $x=6y^2$, we have $4p=6$, so $p=\frac{3}{2}$. Therefore, the focus is at $\left(\frac{1}{4p},0\right)=\left(\frac{1}{24},0\right)$ and the directrix is the line $x=-\frac{1}{4p}=-\frac{1}{24}$. Therefore, the answer is (A).

Graph Parabolas with Vertices at the Origin Find the Focus x=6y2x = 6 y ^ { 2 }x=6y2

Graph Parabolas with Vertices at the Origin
Find the Focus $x = 6 y ^ { 2 }$