Question

From a point P(1, 2), two tangents are drawn to a hyperbola H in which one tangent is drawn to each arm 0f the hyperbola. If the equations of asymptotes of hyperbola H are $\sqrt{3}x-y+5=0and\sqrt{3}x+y-1=0$, then eccentricity of H is

• A. 2
• B.
  
• C.
  
• D.

Answer 1

The correct option is B


Since $c_1{c}_2(a_1{a}_2+b_1{b}_2)<0$, therefore origin lies in acute angle and P(1, 2) lies in obtuse angle.
Acute angle between the asymptotes is $\frac{\pi }{3}$
Hence, $e=sec\frac{\theta }{2}=sec\frac{\pi }{6}=\frac{2}{\sqrt{3}}$