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

Options

A. `(x)/(x_(1)+x_(2))+(y)/(y_(1)+y_(2))=1`
B. `(x)/(x_(1)-x_(2))+(y)/(y_(1)-y_(2))=1`
C. `(x)/(y_(1)+y_(2))+(y)/(x_(1)+x_(2))=1`
D. `(x)/(y_(1)-y_(2))+(y)/(x_(1)-x_(2))=1`

Explanation

The mid-point of the chord is `((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2))`
The equation of the chord in terms of its mid-point is
or, `x((y_(1)+y_(2))/(2))+y((x_(1)+x_(2))/(2))=2((x_(1)+x_(2))/(2))((y_(1)+y_(2))/(2))`
`impliesx(y_(1)+y_(2))+y(x_(1)+x_(2))=(x_(1)+x_(2))(y_(1)+y_(2))`
`implies(x)/(x_(1)+x_(2))+(y)/(y_(1)+y_(2))=1`