If the equation of asymptotes of a hyperbola is $3 \mathrm{x}^2+10 \mathrm{xy}+3 \mathrm{y}^2+5 \mathrm{x}+6 \mathrm{y}+\mu=0$, then eccentricity of the hyperbola is/are
(A) $\sqrt{5}$
(B) $\frac{\sqrt{5}}{2}$
(c) $\sqrt{3}$
(D) $\frac{\sqrt{3}}{2}$
What I tried: Angle between pair of straight lines is given by $$\tan\theta=2\dfrac{\sqrt{h^2-ab}}{|a+b|}\\ =\frac43$$ Now I know that eccentricity is given by $$e=\sec(\frac{\theta}{2})$$
By half angle identity, $\sec\theta=\frac{\sqrt5}{2}$
So $$e=\dfrac{\sqrt5}{2}$$
But the given answer is A,B
What am I missing?