The equation& of the chord of the hyperbola 25x^ 2 - 16y^ 2 = 400 ,...

The equation& of the chord of the hyperbola

25x^{2} - 16y^{2} = 400

, which is bisected at the point

( 6, 2 ) ,

Options

A $16x - 75y = 418$
B $75x - 16y = 418$
C $25x - 4y = 400$
DNone of these

Correct answer

B. $75x - 16y = 418$

Step-by-step solution

Given equation of hyperbola is $25x^{2} - 16y^{2} = 400 .$

If $( 6, 2 )$ is the mid-point of the chord, then equation of chord is $T = {S}_{1} .$

$⇒ 25\left(6x\right) - 16\left(2y\right) - 400 = \left(25\right)\left(36\right) - 16 ( 4 ) - 400$

$⇒ 75x - 16y = 418$ .

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