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Find the equation of the chord of the hy...

Find the equation of the chord of the hyperbola `25 x^2-16 y^2=400` which is bisected at the point (5, 3).

A

`115x - 117y = 17`

B

`125x - 48y = 481`

C

`127x + 33y = 341`

D

`15x - 121y = 105`

Text Solution

Verified by Experts

The correct Answer is:
B
`S = 25 x^(2) - 16 y^(2) - 400 = 0`
Equation of required chord is `S_(1) =T` (i)
Here, `S_(1) = 25(5)^(2) - 16(3)^(2) - 400`
`= 625 - 144 - 400 = 81`
and `T = 25 xx_(1) - 16 yy_(1) - 400`, where `x_(1) = 5, y_(1) =3`
`= 25(x)(5) - 16(y)(3) -400 - 125 x - 48y - 400`
so from (i), required chord is
`125x - 48y - 400 = 81`
or `125x - 48y = 481`
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