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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:
5y2 = 24x
Solution
Given equation of the parabola is 5y2 = 24x.
∴ y2 = `24/5"x"`
Comparing this equation with y2 = 4ax, we get
4a = `24/5`
∴ a = `6/5`
Co-ordinates of focus are S(a, 0), i.e., S`(6/5, 0)`
Equation of the directrix is x + a = 0.
i.e., `"x" + 6/5` = 0, i.e., 5x + 6 = 0
Length of latus rectum = 4a = `4(6/5) = 24/5`
Co-ordinates of end points of latus rectum are (a, 2a) and (a, –2a), i.e., `(6/5, 12/5)` and `(6/5, (-12)/5)`.
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