JEE Advance - Mathematics (2007 - No. 30)
A hyperbola, having the transverse axis of length $$2\sin \theta ,$$ is confocal with the ellipse $$3{x^2} + 4{y^2} = 12.$$ Then its equation is
$${x^2}\cos e{c^2}\theta - {y^2}{\sec ^2}\theta = 1$$
$${x^2}\cos e{c^2}\theta - {y^2}{\sec ^2}\theta = 1$$
$${x^2}{\sin ^2}\theta - {y^2}co{s^2}\theta = 1$$
$${x^2}{\cos ^2}\theta - {y^2}{\sin ^2}\theta = 1$$