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Question

Find the asymptotes of the hyperbola 2x2−3xy−2y2+3x−y+8=0. Also find the equation to the conjugate hyperbola & the equation of the principal axes of the curve.

A
x2y+1=0;2x+y+1=0;2x23xy2y2+3xy6=0;3xy+2=0;x3y=0
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B
x+2y1=0;2x+y+1=0;2x23xy2y2+3xy+6=0;3xy+2=0;x+3y=0
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C
x2y+1=0;2x+y+1=0;2x23xy2y2+3xy6=0;3xy+2=0;x+3y=0
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D
x2y+1=0;2xy+1=0;2x23xy2y2+3xy+6=0;3xy2=0;x3y=0
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Solution

The correct option is C x2y+1=0;2x+y+1=0;2x23xy2y2+3xy6=0;3xy+2=0;x+3y=0
Let equation of asymptotes are
2x23xy2y2+3xy+8+λ=0
As it represents two straight lines
4(8+λ)+9412+92(8+λ)94=0
λ=7
So asymptotes are 2x23xy2y2+3xy+1=0
2y - x - 1 = 0 & 2x + y + 1 = 0
and the equation of conjugate hyperbola will be
2x23xy2y2+3xy+814=0.

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