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The x and y-intercept of the chord of hyperbola \mathrm{9 x^2-4 y^2=36} are \mathrm{\alpha} and \mathrm{\beta}. The midpoint of chord is (10,10). Then \mathrm{9 \alpha+4 \beta} is equal to ___________.

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

3


Answers (1)

best_answer

S=9 x^2-4 y^2-36=0

Equation of required chord is S_1=T                                   ...(i)

Here, S_1=9(10)^2-4(10)^2-36=900-400-36=464$ and $T=90 x-40 y-36

So from (i), the equation of required chord is

90 x-40 y-36=464 \Rightarrow 90 x-40 y=500

x-intercept is \alpha=\frac{50}{9}

And, y-intercept is \beta=\frac{-50}{4}

\therefore 9 \alpha+4 \beta=0

Posted by

sudhir.kumar

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