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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:
3y2 = –16x
Solution
Given equation of the parabola is 3y2 = –16x.
∴ y2 = `-16/3"x"`
Comparing this equation with y2 = – 4ax, we get
4a = `16/3`
∴ a = `4/3`
Co-ordinates of focus are S(–a, 0), i.e., S`(-4/3, 0)`
Equation of the directrix is x – a = 0,
i.e., `"x" - 4/3` = 0 i.e., 3x – 4 = 0
Length of latus rectum = 4a = `4(4/3) = 16/3`
Co-ordinates of end points of latus rectum are (–a, 2a) and (–a, –2a), i.e., `(-4/3, 8/3)` and `(-4/3, -8/3)`.
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