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Question
Find co-ordinate of focus, equation of directrix, length of latus rectum and the co-ordinate of end points of latus rectum of the parabola:
3x2 = 8y
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Solution
Given equation of the parabola is 3x2 = 8y.
∴ x2 = `8/3y`
Comparing this equation with x2 = 4by, we get
4b = `8/3`
∴ b = `2/3`
Co-ordinates of focus are S(0, b), i.e., `"S"(0, 2/3)`
Equation of the directrix is y + b = 0,
i.e., `y + 2/3` = 0, i.e., 3y + 2 = 0
Length of latus rectum = 4b = `4(2/3) = 8/3`
Co-ordinates of end points of latus rectum are (2b, b) and (–2b, b), i.e., `(4/3, 2/3)` and `(-4/3, 2/3)`.
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