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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:
2y2 = 17x
Solution
Given equation of the parabola is 2y2 = 17x
∴ y2 = `17/2"x"`
Comparing this equation with y2 = 4ax, we get
4a = `17/2`
∴ a = `17/8`
Co-ordinates of focus are S(a, 0), i.e., S`(17/8, 0)`
Equation of the directrix is x + a = 0
i.e., `"x" + 17/8` = 0, i.e., 8x + 17 = 0
Length of latus rectum = 4a = `4(17/8) = 17/2`
Co-ordinates of end points of latus rectum are (a, 2a) and (a, –2a)
i.e., `(17/8, 17/4)` and `(17/8, -17/4)`
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