If the ellipse \( x^{2}+\lambda^{2} y^{2}=\lambda^{2} a^{2} ; \lamb...

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If the ellipse \( x^{2}+\lambda^{2} y^{2}=\lambda^{2} a^{2} ; \lambda^{2}1 \) is confocal
\( \mathrm{P}^{142} \) with the hyperbola \( x^{2}-y^{2}=a^{2} \), then

W
(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 latus rectum of ellipse and hyperbola is \( 1: 3 \)
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