The correct option is B Asymptotes: 3x2−5xy−2y2+5x+11y−12=0
Given: Hyperbola 3x2−5xy−2y2+5x+11y−8=0
To Find: Equation of asymptotes and conjugate hyperbola
3x2−5xy−2y2+5x+11y−8=0
Equation of asymptotes is 3x2−5xy−2y2+5x+11y+c=0
Since, it's a pair of straight lines, the determinant value will be zero.
△=abc+2fgh−af2−bg2−ch2=0
a=3,h=−52,b=−2,g=52,f=112
⇒△=(3)(−52)c+2(112)(52)(−52)−3(112)2−(−2)(52)2−c(−52)2=0
⇒△=−6c−2754−3634+504−25c4=0
⇒c=−58849=−12
Asymptote equation is 3x2−5xy−2y2+5x+11y−12=0
We know that, the equation of asymptote differs by the equation of hyperbola by some constant. It will differ with the conjugate hyperbola equation by same constant value.
3x2−5xy−2y2+5x+11y−8+conjugate hyperbola=2(3x2−5xy−2y2+5x+11y−12)
conjugate hyperbola=3x2−5xy−2y2+5x+11y−16=0