The Equation Of A Line Passing Through The Center Of A Rectangular Hyperbola Is x – Y – 1 = 0, If One Of Its Asymptotes Is 3x – 4y – 6 = 0, The Equation Of The Other Asymptote Is  

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The equation of a line passing through the center of a rectangular hyperbola is x – y – 1 = 0, if one of its asymptotes is 3x – 4y – 6 = 0, the equation of the other asymptote is



Correct option is

4x + 3y + 17 = 0

We know that asymptotes of rectangular hyperbola are mutually perpendicular, thus other asymptote should be 4x + 3y + λ = 0.

Intersection point of asymptotes is also the center of the hyperbola. Hence intersection point of 4x + 3y + λ = 0 and 3x – 4– 6 = 0 should lie on the line x – y – 1 = 0, using it λ can be easily obtained.



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