If the product of the perpendicular distances from any point on the hyperbola x^2 a^2 - y^2 b^2 =1 to its asymptotes is 6 and eccentricity of the hyperbola is 3 , then the length of the conjugate axis of the hyperbola is

Step-by-step solution

P Q= | a b -a b b^2+a^2 | and P R= | a b +a b b^2+a^2 | According to question, a b( - ) a^2+b^2 a b( + ) a^2+b^2 =6 a^2 b^2 ( ^2 - ^2 ) (a^2+b^2 ) =6 a^2 b^2 a^2 e^2 =6 [ a^2+b^2=a^2 e^2 ] array ll & b^2=6 e^2=6 3=18 & a^2+b^2=a^2 e^2 array a^2+18=a^2 3 a^2=9 a=3 Length of transverse axis =2 3=6