Give the focus, directrix, and axis for the parabola.
-$$y ^ { 2 } = 28 x$$
A) $( 0,7 ) , y = - 7 , y$-axis
B) $( 7,0 ) , x = - 7 , x$-axis
C) $( 7,7 ) , x = 7 , x$-axis
D) $( 7,0 ) , x = - 7 , y$-axis

Question

Quizplus · Accepted Answer

The given equation is $y^2 = 28x$, which is a standard form of a parabola that opens to the right. The general form for such a parabola is $y^2 = 4ax$, where $a$ is the distance from the vertex to the focus and also to the directrix. Comparing, we find $4a = 28$, so $a = 7$. Therefore, the focus is $(a, 0) = (7, 0)$, the directrix is $x = -a = -7$, and the axis of symmetry is the $y$-axis, which matches option B.

Give the Focus, Directrix, and Axis for the Parabola y2=28xy ^ { 2 } = 28 xy2=28x

Give the Focus, Directrix, and Axis for the Parabola $y ^ { 2 } = 28 x$