The eccentricity of the hyperbola which passes through the points (3,0) and (3 2 , 2) is

Step-by-step solution

Given that the hyperbola passes through the points (3, 0) and (3 2 , 2) , we take the standard form x^2 a^2 - y^2 b^2 = 1 . Substituting point (3, 0) yields 9 a^2 = 1 , thus a^2 = 9 . With a^2 known, inserting point (3 2 , 2) gives 18 9 - 4 b^2 = 1 , which simplifies to 2 - 4 b^2 = 1 and leads to b^2 = 4 . The eccentricity follows from b^2 = a^2(e^2 - 1) . Substituting known values, 4 = 9(e^2 - 1) , so e^2 = 13 9 and e = 13 3 . The correct choice is C .