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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:
x2 = –8y
Solution
The equation of the parabola is x2 = –8y.
Comparing with x2 = – 4by, we get,
4b = 8
∴ b = 2
The coordinates of the focus are (0, – b), i.e. (0, – 2).
The equation of the directrix is
y – b = 0, i.e. y – 2 = 0
The length of the latus rectum = 4b = 8
The coordinates of the end points of the latus rectum are (2b, –b) and (–2b, –b) i.e., (4, – 2) and (– 4, – 2).
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