Find the coordinates of the focus, axis of the parabola,

Question:

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for $x^{2}=-16 y$

Solution:

The given equation is $x^{2}=-16 y$.

Here, the coefficient of is negative. Hence, the parabola opens downwards.

On comparing this equation with $x^{2}=-4$ ay, we obtain

$-4 a=-16 \Rightarrow a=4$

$\therefore$ Coordinates of the focus $=(0,-a)=(0,-4)$

Since the given equation involves $x^{2}$, the axis of the parabola is the $y$-axis.

Equation of directrix, $y=$ a i.e., $y=4$

Length of latus rectum $=4 a=16$

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