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If from a variable point ‘P’ on the line x-2y+1=0 pair of tangents are drawn to the parabola y 2 =8x then prove that the chord of contact passes through a fixed point, also find that point.

If from a variable point ‘P’ on the line x-2y+1=0 pair of tangents are drawn to the parabola y2=8x then prove that the chord of contact passes through a fixed point, also find that point.

Grade:upto college level

1 Answers

Pratik Tibrewal
askIITians Faculty 37 Points
7 years ago
Let the point be (h,k)
then h - 2k + 1 = 0 ----- (1)
equation of chord of contact will be T = 0, i.e, yk = 8 (x + h)/2
yk = 4x + 4h ---- (2)
Put value of h from equation (1) into equation (2)
yk = 4x + 4(2k - 1)
=> k ( y - 8) = 4(x - 1)
This is equation of family of lines.
Fixed point is (1, 8)


Thanks and Regards,
Pratik Tibrewal
askiitian faculty
BTech IITG

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