length of chord of contact of tangents drawa from point (x1,y1) to the parabola y2=4ax is how is this result derived?

Dear Student,

Consider the two points on the parabola are P(at₁², 2at₁) and Q (a_t2², 2at₂).
Now write the equation of tangents at P and Q and find their point of intersection.
If they intersect at (x₁,y₁), then you will get x₁ = at₁t₂ and y₁ = a(t₁ + t₂).
Now write the distance formula for PQ and replace t₁t₂ by x₁/a and (t₁ + t₂) by y₁/a.

You will get the derived result.

Thanks.