If the ellipse ; is confocal with the hyperbola

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

If the ellipse

x^2 + \lambda^2 y^2 = \lambda^2 a^2

;

\lambda^2 > 1

is confocal with the hyperbola

x^2 - y^2 = a^2

, then (1) ratio of eccentricities of ellipse and hyperbola is

1:\sqrt{3}

(2) ratio of major axis of ellipse and transverse axis of hyperbola is

\sqrt{3}:1

(3) The ellipse and hyperbola cuts each other orthogonally (4) ratio of length of latusrectum of ellipse and hyperbola is

1:3