Give the focus, directrix, and axis for the parabola.
-$$- \frac { 1 } { 36 } x ^ { 2 } = y$$
A) $( 0 , - 9 ) , y = 9 , x$-axis
B) $( 0 , - 9 ) , y = 9 , y$-axis
C) $( 0,9 ) , y = - 9 , y$-axis
D) $( - 18,0 ) , x = 9$, x-axis

Question

Quizplus · Accepted Answer

The given equation of the parabola is $-\frac{1}{36}x^2 = y$, which can be rewritten as $y = -\frac{1}{36}x^2$. This is a vertically oriented parabola (opens downwards) with its vertex at the origin (0,0). The coefficient of $x^2$ is $-\frac{1}{4p}$, where $p$ is the distance from the vertex to the focus and also from the vertex to the directrix. Comparing $-\frac{1}{36} = -\frac{1}{4p}$, we find $p = 9$. Since the parabola opens downwards, the focus is at $(0, -9)$ and the directrix is $y = 9$. The axis of symmetry is the y-axis because the parabola opens along the vertical direction.

Give the Focus, Directrix, and Axis for the Parabola −136x2=y- \frac { 1 } { 36 } x ^ { 2 } = y−361​x2=y

Give the Focus, Directrix, and Axis for the Parabola $- \frac { 1 } { 36 } x ^ { 2 } = y$