The correct option is B 6x2−xy−y2−23x+4y+15=0
The combined equation of the asymptotes is (2x−y−3)(3x+y−7)=0
⇒6x2−xy−y2−23x+4y+21=0
Let the equation of the hyperbola be 6x2−xy−y2−23x+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 6x2−xy−y2−23x+4y+15=0.