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  4. Equation of the chord of the hyperbola 25x2 -16y2 = 400 which is bisected at the point (6, 2) is

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Q. Equation of the chord of the hyperbola $25x^2 -16y^2 = 400$ which is bisected at the point (6, 2) is

VITEEEVITEEE 2014

Solution:

Given hyperbola is
$25x^{2} - 16y^{2} = 400$
If (6, 2) is the midpoint of the chord, then equation of chord is $T = S_1$
$\Rightarrow 25 \left(6x\right) - 16 \left(2y\right) = 25 \left(36\right) - 16 \left(4\right)$
$\Rightarrow 75x - 16y = 450 - 32$ (divide by 2)
$\Rightarrow 75x - 16y = 418$