A hyperbola having the transverse axis of length, 2 has the same foci as that of the ellipse, 3 x 2 + 4 y 2 = 12 then this hyperbola does not pass through which of the following points?

Step-by-step solution

Equation of ellipse : x 2 4 + y 2 3 = 1 ⇒ e = 1 - 3 4 = 1 2 Foci of the ellipse: ± 2 × 1 2 , 0 i.e., ± 1 , 0 For hyperbola: Length of the transverse axis = 2 a = 2 ⇒ a = 1 2 Foci of hyperbola ± 1 , 0 ⇒ a e = 1 b 2 = a 2 e 2 - a 2 = 1 - 1 2 = 1 2 Equation of hyperbola : x 2 1 / 2 - x 2 1 / 2 = 1 ⇒ x 2 - y 2 = 1 2 ⇒ 2 x 2 - 2 y 2 = 1 Only the point, 3 2 , 1 2 does not satisfy the above equation.