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Question

The equation of a hyperbola, conjugate to the hyperbola x2+3xy+2y2+2x+3y+1=0, is

A
x2+3xy+2y2+2x+3y+1=0
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B
x2+3xy+2y2+2x+3y+2=0
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C
x2+3xy+2y2+2x+3y+3=0
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D
x2+3xy+2y2+2x+3y+4=0
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Solution

The correct option is B x2+3xy+2y2+2x+3y+2=0
We know that,
Equation of hyperbola + Equation of conjugate
hyperbola = 2(Equation of asymptotes)
Equation of conjugate hyperbola
= 2 Equation of asymptotes - Equation of hyperbola
C(x, y) = 2A(x, y) – H(x, y) …… (i)
H(x,y)x2+3xy+2y2+2x+3y=0
Equation of asymptotes is
x2+3xy+2y2+2x+3y+λ=0
Δ=0,abc+2fghaf2bg2ch2=0,thenλ=1
A(x,y)x2+3xy+2y2+2x+3y+1=0
C(x,y)x2+3xy+2y2+2x+3y+2=0[from equation (i)]

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