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prove that the equation of the chord of the hyperbola xy=c^2 which is bisected at the point (2c,3c) is 3x+2y=12c

prove that the equation of the chord of the hyperbola xy=c^2 which is bisected at the point (2c,3c) is 3x+2y=12c
 

Grade:11

1 Answers

subrat
61 Points
6 years ago
This can be solved using transformation of curves. Equation of chord when mid point is given is by T=S1 where T is the transformed equation and S1 is the value of curve when point is put into it. Transformation for xy=(x1y+xy1)/2. So,
(2cy+3cx)/2 – c2 = 6c2 – c2 . Hence, the answer is 3x+2y=12c.
 

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