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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

2 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
9 years ago
Hi,

Find out the equation of focal chord as it passes through point (at^2 , 2at ) and (a,0) which is the focus.

Now if this line cuts the curve again than let that point be (at1^2 , 2at1).

Satisfy this point in the equation of focal chord and find the relation between t1 and t.

Now we have the extrimities of focal chord in terms of t. Using distance formula find the length. Which will be ur answer.
Nishant Vora IIT Patna
askIITians Faculty 2467 Points
9 years ago
Hi Student,

If one of the extremities is P(at^2 , 2at )
Then for focal chord we have this relation t1t2 = -1

So the other extremity will be Q (\frac{a}{t^2},\frac{-2a}{t})

Now apply distance formula to find out the length of focal chord i.e PQ

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