If the coordinates of a variable point be where is the variable quantity

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

Problem

If the coordinates of a variable point

P

\left(t + \frac{1}{t}, t - \frac{1}{t}\right)

where

t

is the variable quantity, then the locus of

P

is (1)

xy = 8

(2)

2x^2 - y^2 = 8

(3)

x^2 - y^2 = 4

(4)

2x^2 + 3y^2 = 5