If the distance between the foci and the distance between the directrices of the hyperbola x² a² - y² b² =1 are in the ratio 3: 2 , then a: b is

Step-by-step solution

Equation of hyperbola is x² a² - y² b² =1 Distance between foci =2 a e and distance between directrices = 2 a e According to question, we have 2 a e 2 a / e = 3 2 array ll & e²= 3 2 & b²=a² (e²-1 ) & b² a² = 3 2 -1= 1 2 & b a = 1 2 & a: b= 2 : 1 array