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)

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.

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

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