Home
Class 12
MATHS
The equation of that chord of hyperbola ...

The equation of that chord of hyperbola `25x^(2)-16y = 400`, whose mid point is (5,3) is

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`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

Equation of the chord of the circle x^(2) + y^(2) - 4x = 0 whose mid-point is (1,0) , is

Let I be the length of the chord of the hyperbola x^(2) - y^(2) = 8 , whose mid-point is (4,2), then I equals

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

The equation of the chord of x^(2)+y^(2)-4x+6y+3=0 whose mid point is (1,-2) is

The equation of chord of the hyperbola 25x^(2)-16y^(2)=400 which is bisected at the point (6,2) is

Equation of the chord of the hyperbola 25x^(2)-16y^(2)=400 which is bisected at the point (6,2) is 75x-ky=418 .Then K=