A) length of the latus rectum is \[4/\sqrt{3}\]
B) asymptotes, intersect at right angles
C) the eccentricity of the conic is \[2/\sqrt{3}\]
D) centre of the conic is \[(2,-1)\]
Correct Answer: B
Solution :
The conic is \[{{x}^{2}}-3{{y}^{2}}-4x-6y-11=0\Rightarrow \] \[{{x}^{2}}-4x+4-3({{y}^{2}}-2y+1)-4+3-11=0\] i.e., \[{{(x-2)}^{2}}-3{{(y-1)}^{2}}=12\] \[\Rightarrow \] \[\frac{{{(x-2)}^{2}}}{12}-\frac{{{(y-1)}^{2}}}{4}=1\] \[\therefore \] \[a=2\sqrt{3},\,b=2\Rightarrow a\ne b\] \[\therefore \] The asymptotes do not intersect at right angles.
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