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If the point (at^2 , 2at ) be exttemity of focal chord of parabola y^2 = 4ax then show length of focalchord is a(t + 1/t^2)

If the point (at^2 , 2at ) be exttemity of focal chord of parabola y^2 = 4ax then show length of focalchord is 
a(t + 1/t^2)

Grade:11

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
Find the eqn of focal chord using the condition that the focal chord passes through the focus(a,0) as well as(at^2 , 2at) by using the two point form of the straight line. Now, find the point of intersection of the straight line then formed with the parabola given. This will result in 2 points, one being(at^2 , 2at) and the other one which is the one that is needed. Use both these points to find the distance between them which will be the length of the focal chord.

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