Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
$x^{2} = - 9 y$

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Solution

The given equation of parabola is $x^{2} = - 9 y$
Which is of the form $x^{2} = - 4 a y .$
$∴ 4 a = 9 \Rightarrow a = \frac{9}{4}$
$∴$ Coordinates of focus are $(0, \frac{- 9}{4})$
Axis of parabola is x = 0
Equation of the directrix is
$y = \frac{9}{4} \Rightarrow 4 y - 9 = 0$
Length of latus rectum $= 4 \times \frac{9}{4} = 9$

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