A hyperbola, having the transverse axis of length , is confocal with the ellipse .…

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

Problem

A hyperbola, having the transverse axis of length

2 \sin \theta

, is confocal with the ellipse

3x^2 + 4y^2 = 12

. Then, its equation is (1)

x^2 \csc^2 \theta - y^2 \sec^2 \theta = 1

(2)

x^2 \sec^2 \theta - y^2 \csc^2 \theta = 1

(3)

x^2 \sin^2 \theta - y^2 \cos^2 \theta = 1

(4)

x^2 \cos^2 \theta - y^2 \sin^2 \theta = 1