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Question

The equation of the hyperbola whose asymptotes are 2xy=3 and 3x+y=7 and passing though the point (1,1) is

A
6x2xyy220x+4y+12=0
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B
6x2xyy223x+4y+15=0
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C
6x2xyy2+20x4y20=0
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D
6x2+xy+y223x4y+19=0
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Solution

The correct option is B 6x2xyy223x+4y+15=0
The combined equation of the asymptotes is (2xy3)(3x+y7)=0
6x2xyy223x+4y+21=0

Let the equation of the hyperbola be 6x2xyy223x+4y+λ=0,

where λ is a constant such that it represents hyperbola which passes through (1,1),
so λ=15.

Hence, the equation of the hyperbola becomes 6x2xyy223x+4y+15=0.

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