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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.
y2 = 10x
Solution
The given equation is y2 = 10x.
Here, the coefficient of x is positive. Hence, the parabola opens towards the right.
On comparing this equation with y2 = 4ax, we obtain
4a = 10 ⇒ a = `5/2`
∴ Coordinates of the focus = (–a, 0) = `(5/2, 0)`
Since the given equation involves y2, the axis of the parabola is the x-axis.
Equation of directrix, x = a i.e., x = `-5/2`
Length of latus rectum = 4a = 10
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