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

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Solution

The given equation is $x^{2} = - 16 y$
Here, the coefficient of $y$ is negative.
Hence the parabola opens downwards.
On comparing this equation with $x^{2} = - 4 a y$
$- 4 a = - 16$
$\Rightarrow a = 4$
$∴$ Coordinates of the focus $= (0, - a) = (0, - 4)$
Axis of the parabola is the $y$ -axis i.e $x = 0$
Equation of directrix $y = a$ i.e., $y = 4$
Length of latus rectum $= 4 a = 16$

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