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Question
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.
x2 = –9y
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Solution
The given equation is x2 = –9y.
Here, the coefficient of y is negative. Hence, the parabola opens downwards.
On comparing this equation with x2 = –4ay, we obtain
4a = 10 ⇒ a = `9/4`
∴ Coordinates of the focus = (0, -a) = `(0, 9/4)`
Since the given equation involves x2, the axis of the parabola is the y-axis.
Equation of directrix, y = a i.e., y = `9/4`
Length of latus rectum = 4a = 9
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