The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$x = 10 y ^ { 2 }$$
A) focus: $\left( \frac { 1 } { 40 } , 0 \right)$
directrix: $x = - \frac { 1 } { 40 }$
B) focus: $\left( 0 , \frac { 1 } { 40 } \right)$
directrix: $y = - \frac { 1 } { 40 }$
C) focus: $\left( \frac { 1 } { 10 } , 0 \right)$
directrix: $x = - \frac { 1 } { 10 }$
D) focus: $\left( \frac { 1 } { 40 } , 0 \right)$
directrix: $x = \frac { 1 } { 40 }$

Question

The Parabola
1 Graph Parabolas with Vertices at the Origin
-$$x = 10 y ^ { 2 }$$
A) focus: $\left( \frac { 1 } { 40 } , 0 \right)$
directrix: $x = - \frac { 1 } { 40 }$ 
B) focus: $\left( 0 , \frac { 1 } { 40 } \right)$
directrix: $y = - \frac { 1 } { 40 }$
C) focus: $\left( \frac { 1 } { 10 } , 0 \right)$
 directrix: $x = - \frac { 1 } { 10 }$ 
D) focus: $\left( \frac { 1 } { 40 } , 0 \right)$
directrix: $x = \frac { 1 } { 40 }$

Quizplus · Accepted Answer

The equation $x = 10y^2$ represents a parabola that opens to the right since it is in the form $x = ay^2$. The focus of such a parabola is at $\left(\frac{1}{4a}, 0\right)$ and the directrix is $x = -\frac{1}{4a}$. Here, $a = 10$, so $\frac{1}{4a} = \frac{1}{40}$, making the focus $\left(\frac{1}{40}, 0\right)$ and the directrix $x = -\frac{1}{40}$, which matches option A.

The Parabola 1 Graph Parabolas with Vertices at the Origin x=10y2x = 10 y ^ { 2 }x=10y2

The Parabola
1 Graph Parabolas with Vertices at the Origin $x = 10 y ^ { 2 }$