The equation of the chord joining two points and on the rectangular hyperbola is

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

Problem

The equation of the chord joining two points

(x_1, y_1)

and

(x_2, y_2)

on the rectangular hyperbola

xy = c^2

is (1)

\frac{x}{x_1 + x_2} + \frac{y}{y_1 + y_2} = 1

(2)

\frac{x}{x_1 - x_2} + \frac{y}{y_1 - y_2} = 1

(3)

\frac{x}{y_1 + y_2} + \frac{y}{x_1 + x_2} = 1

(4)

\frac{x}{y_1 - y_2} + \frac{y}{x_1 - x_2} = 1