Give the focus, directrix, and axis for the parabola.
-$x = 10 y ^ { 2 }$
A) $\left( 0 , \frac { 1 } { 40 } \right) , \mathrm { y } = - \frac { 1 } { 40 } , \mathrm { y }$-axis
B) $\left( \frac { 1 } { 10 } , 0 \right) , x = - \frac { 1 } { 10 } , x$-axis
C) $\left( \frac { 1 } { 40 } , 0 \right) , x = \frac { 1 } { 40 } , x$-axis
D) $\left( \frac { 1 } { 40 } , 0 \right) , x = - \frac { 1 } { 40 } , x$-axis

Question

Quizplus · Accepted Answer

The equation $x = 10y^2$ can be rewritten as $y^2 = \frac{1}{10}x$, which is a parabola opening to the right. The general form for such a parabola is $y^2 = 4px$, where $p$ is the distance from the vertex to the focus and also from the vertex to the directrix. Comparing the given equation to the general form, $4p = \frac{1}{10}$, so $p = \frac{1}{40}$. The focus is at $(p, 0)$ or $\left(\frac{1}{40}, 0\right)$, the directrix is $x = -p$ or $x = -\frac{1}{40}$, and the axis of symmetry is the x-axis.

Give the Focus, Directrix, and Axis for the Parabola x=10y2x = 10 y ^ { 2 }x=10y2

Give the Focus, Directrix, and Axis for the Parabola $x = 10 y ^ { 2 }$