A hyperbola whose transverse axis is along the major axis of the conic, {{{x^2}} \over 3} + {{{y^2}} \over 4} = 4 and has vertices at the foci of this conic. If the eccentricity of the hyperbola is {3 \over 2}, then which of the following points does NOT lie on it?

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Answer: D. \left( {5,2\sqrt 3 } ight) {{{x^2}} \over {12}} + {{{y^2}} \over {16}} = 1 e = \sqrt {1 - {{12} \over {16}}} = {1 \over 2} Foci (0, 2) & (0, - 2) So, transverse axis of hyperbola = 2b = 4 \Rightarrow b = 2 & a2 = 12 (e2 - 1) \Rightarrow a2 = 4\left( {{9 \over 4} - 1} ight) \Rightarrow a2 = 5 	herefore It's equation is {{{x^2}} \over 5} - {{{y^2}} \over 4} = - 1 The point (5, 2\sqrt 3 ) does not satisfy the above equation.

A hyperbola whose transverse axis is along the major axis of the conic, $${{{x^2}} \over 3} + {{{y^2}} \over 4} = 4$$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $${3 \over 2},$$ then which of the following points does NOT lie on it?

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