Question

Which of the following can not be the equation of tangent to a rectangular hyperbola
$xy=16$

• A. $x+y=8$
• B. $x+y=-8$
• C. $4x-y=2$
• D. $4x+y=16$

Answer 1

The correct option is C $4x-y=2$

Property: Slope of the tangent to a rectangular hyperbola is always negative.
A) $4x+y=16\Rightarrow m=-4$
It can be the slope of tangent for given hyperbola

B) $4x-y=2\Rightarrow m=4$
It can not be the slope of tangent for given hyperbola

C) $x+y=8\Rightarrow m=-1$
It can be the slope of tangent for given hyperbola

D) $x+y=-8\Rightarrow m=-1$
It can be the slope of tangent for given hyperbola
Hence, the correct answer is Option b.