If any point on a hyperbola is (3 , 2 ) , then what is the eccentricity of the hyperbola?

Step-by-step solution

Let equation of hyperbola is x^2 a^2 - y^2 b^2 =1 then eccentricity e= 1+ a^2 b^2 Now, as point (3 , 2 ) lies on hyperbola then, 3^2 ^2 a^2 - 2^2 ^2 b^2 =1 9 ^2 a^2 - 4 ^2 b^2 =1 This is true for a^2=9 and b^2=4 eccentricity (e)= 1+ 9 4 = 13 2