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

Question

Equation of the chord of the hyperbola 25x2 -16y2 = 400 which is bisected at the point (6, 2) is (A) 6x - 7y = 418 (B) 75x - 16y = 418 (C) 25x - 4y = 400 (D) None of these

Tardigrade Admin · Accepted Answer

Given hyperbola is 25x2 - 16y2 = 400 If (6, 2) is the midpoint of the chord, then equation of chord is T = S1 ⇒ 25 (6x) - 16 (2y) = 25 (36) - 16 (4) ⇒ 75x - 16y = 450 - 32 (divide by 2) ⇒ 75x - 16y = 418

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

6x - 7y = 418

75x - 16y = 418

25x - 4y = 400

None of these

Given hyperbola is
$25 x^{2} - 16 y^{2} = 400$
If (6, 2) is the midpoint of the chord, then equation of chord is $T = S_{1}$
$\Rightarrow 25 (6 x) - 16 (2 y) = 25 (36) - 16 (4)$
$\Rightarrow 75 x - 16 y = 450 - 32$ (divide by 2)
$\Rightarrow 75 x - 16 y = 418$

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