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Question

Find the coordinates of the points on the parabola y2=2x whose focal distance is 52.

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Solution

Comparing above parabola with y2=4ax, we get a=12
So focal distance is given by, x+a=52 (given )
x+12=52x=2
Substitute x=2 in the given parabola,
y2=2x=22y=±2

Hence coordinate of the points on the parabola whose focal distance is 52 units are (2,2) and (2,2)

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