A hyperbola whose transverse axis is along the major axis of the conic x 2 3 + y 2 4 = 4 and has vertices at the foci of the conic. If the eccentricity of the hyperbola is 3 2 , then which of the following points does not lie on the hyperbola ?

Step-by-step solution

Given conic is x 2 12 + y 2 16 = 1 e =   1 - 12 16 = 1 2 Foci 0 , 2 and 0 , - 2 . So, transverse axis of hyperbola = 2 b = 4 . ⇒ b = 2 Given e = 3 2 And a 2 = b 2 e 2 - 1 ⇒ a 2 = 4   9 4 - 1 ⇒ a 2 = 5 ∴  The equation of hyperbola is x 2 5 - y 2 4 = - 1 . Now, Check options. Clearly, the point 5 , 2 3 does not satisfy above equation.