The equation of the chord of the hyperbola 25x² -1 6 y² = 400 that is bisected at point (5,3) is:

Correct Answer is : 125x−48y=481125x-48y =481125x−48y=481

Correct Answer is : 125x−48y=481125x-48y =481125x−48y=481

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VITEEE 2019 Paper

Section: Mathematics

Question : 106 of 125

Marks: +1, -0

25x^2 -1 6 y^2 = 400

that is bisected at point (5,3) is:

Solution:

The equation of the chord, having mid-point as

(x_1, y_1)

, of the hyperbola

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1

is given by

T=S_1

....(i)

where,

T=\frac{xx_1}{a^2}-\frac{yy_1}{b^2}-1

and

S_1=\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}-1

According to the question,

(x_1,y_1) = (5, 3)

and

a^2= 16,b^2 = 25

25x^2- 16y^2 =400

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

\therefore \frac{5x}{16}-\frac{3y}{25}=\frac{25}{16}-\frac{9}{25}

[Using (i)]

\Rightarrow 125x- 48y = 625 - 144

\Rightarrow 125x - 48y = 481

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