Equation of the chord of the hyperbola 25 x 2 − 16 y 2 = 400 which is bisected at the point (6, 2), is Options: A . &nbsp16x – 75y = 418 B . &nbsp75x - 16y = 418 C . &nbsp25x - 4y = 400 D . &nbspNone of these

Answer: Option B : B Equation of hyperbola is 25 x 2 − 16 y 2 = 400 ⇒ x 2 16 − y 2 25 = 1 Chord is bisected at (6, 2) ∴ 6 x 16 − 2 y 25 = 6 2 16 − 2 2 25 ⇒ 75 x − 16 y = 418

Equation of the chord of the hyperbola 25x2−16y2=400 which is bisect

Question

Equation of the chord of the hyperbola

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

which is bisected at the point (6, 2), is

Options:

A . 16x – 75y = 418

B . 75x - 16y = 418

C . 25x - 4y = 400

D . None of these

Answer: Option B
:
B
Equation of hyperbola is

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

\Rightarrow

\frac{x^{2}}{16} - \frac{y^{2}}{25} = 1

Chord is bisected at (6, 2)

∴

\frac{6 x}{16} - \frac{2 y}{25} = \frac{6^{2}}{16} - \frac{2^{2}}{25}

\Rightarrow

75 x - 16 y = 418

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