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length of chord of contact of tangents drawa from point (x1,y1) to the parabola y 2 =4ax is how is this result derived?

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

Grade:12

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
5 years ago
Dear Student,

Consider the two points on the parabola are P(at12, 2at1) and Q (at22, 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.

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