Question

If the curve $xy=R^2-16$ represents a rectangular hyperbola whose branches lie only in the quadrant in which abscissa and ordinate are opposite in sign, then

• A. $|R|<4$
• B. $|R|\ge 4$
• C. $|R|=4$
• D. $|R|=5$

Answer 1

The correct option is A $|R|<4$

Given $xy=R^2-16$
any point on this curve will be $(x_1,y_1)$
$\because x_1,y_1$ are opposite in sign
$\therefore x_1{y}_1<0\Rightarrow R^2-16<0\Rightarrow |R|<4$