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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 = 6y
Solution
The given equation is x2 = 6y.
Here, the coefficient of y is positive. Hence, the parabola opens upwards.
On comparing this equation with x2 = 4ay, we obtain
4a = 6 = a = `3/2`
∴ Coordinates of the focus = (0, a) = `(0, 3/2)`
Since the given equation involves x2, the axis of the parabola is the y-axis.
Equation of directrix, y= -a i.e., y = `-3/2`
Length of latus rectum = 4a = 6
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