Give the focus, directrix, and axis for the parabola.
-$$\mathrm { y } ^ { 2 } = 4 \mathrm { x }$$
A) $( 1,0 ) , x = - 1 , x$-axis
B) $( 1,0 ) , x = - 1 , y$-axis
C) $( 0,1 ) , y = - 1 , y$-axis
D) $( 1,1 ) , x = 1 , x$-axis

Question

Quizplus · Accepted Answer

The given equation $y^2 = 4x$ represents a parabola that opens to the right. The standard form of a parabola opening to the right is $y^2 = 4px$, where $p$ is the distance from the vertex to the focus and also to the directrix. Here, $4p = 4$, so $p = 1$. The vertex is at the origin $(0,0)$, so the focus, being $p$ units to the right of the vertex, is at $(1,0)$. The directrix is a vertical line $p$ units to the left of the vertex, which is $x = -1$. The axis of the parabola is the line that passes through the focus and is perpendicular to the directrix, which is the $x$-axis in this case.

Give the Focus, Directrix, and Axis for the Parabola y2=4x\mathrm { y } ^ { 2 } = 4 \mathrm { x }y2=4x

Give the Focus, Directrix, and Axis for the Parabola $\mathrm { y } ^ { 2 } = 4 \mathrm { x }$