Find the length of the normal chord which subtends an angle of `90^@` at the vertex of the parabola `y^2=4x` .

Explanation

Let `PQ` is the common chord.

Then, at any point coorinates of `P` and `Q` are `(t1^2,2t1)` and `(t2^2,2t2)`
As the chord subtends an angle of `90^@`, relation between t1 and t2 will be,

`t2=-t1-2/(t1)` `-> Eq(1)`

If O is the origin, then OP and OQ are perpendicular to each other. In that case, both their slopes multiplication will be -1.

Thus,

`(2t1)/(t1^2)**(2t2)/(t2^2)=-1`

`=>t1.t2=-4 ->Eq(2)`

Putting values of t2 from Eq(1)

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