If and are the eccentricities of the hyperbola and

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

Problem

e

and

e'

are the eccentricities of the hyperbola

\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1

and

\frac{x^2}{b^2} - \frac{y^2}{a^2} = 1

, then the point

\left(\frac{1}{e}, \frac{1}{e'}\right)

lies on the circle (1)

x^2 + y^2 = 1

(2)

x^2 + y^2 = 2

(3)

x^2 + y^2 = 3

(4)

x^2 + y^2 = 4