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Question
Answer the following:
For the following parabola, find focus, equation of the directrix, length of the latus rectum, and ends of the latus rectum:
5x2 = 24y
Solution
The equation of the parabola is 5x2 = 24y
i.e., x2 = `24/5"y"`
Comparing with x2 = 4by, we get
4b = `24/5`
∴ b = `6/5`
(1) Focus = (0, b) = `(0, 6/5)`
(2) The equation of directrix is y + b = 0
∴ `"y" + 6/5` = 0
∴ 5y + 6 = 0
(3) Length of latus rectum = 4b = `4(6/5) = 24/5`
(4) Ends of latus rectum are (±2b, b) = `(± 12/5, 6/5)`.
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