The equations of the transverse and conjugate axes of a hyperbola are and…

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

Problem

The equations of the transverse and conjugate axes of a hyperbola are

x + 2y - 3 = 0

and

2x - y + 4 = 0

respectively and their respective lengths are

\sqrt{2}

and

\frac{2}{\sqrt{3}}

. The equation of the hyperbola is (1)

2(x + 2y - 3)^2 - 3(2x - y + 4)^2 = 5

(2)

2(2x - y + 4)^2 - 3(x + 2y - 3)^2 = 5

(3)

2(x + 2y - 3)^2 - 3(2x - y + 4)^2 = 1

(4)

2(2x - y + 4)^2 - 3(x + 2y - 3)^2 = 1