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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:
y2 = –20x
Solution
The equation of the parabola is y2 = –20x.
Comparing with y2 = –4ax, we get
4a = 20
∴ a = 5
The coordinates of the focus are (– a, 0) i.e (– 5, 0)
The equation of the directrix is x – a = 0 i.e. x – 5 = 0
Length of latus rectum = 4a = 20
The coordinates of the end points of latus rectum are (–a, 2a) and (– a, – 2a) i.e. (– 5, 10) and (– 5, –10).
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