Question

Tangents is drawn to a rectangular hyperbola
$xy=9\text{at point}(1,9).$
The area of the triangle formed by tangents and its intercepts is

• A. $4.5$ sq. units.
• B. $36$ sq. units.
• C. $9$ sq. units.
• D. $18$ sq. units.

Answer 1

The correct option is D $18$ sq. units.

Given, $xy=9\Rightarrow c=3$
Area of triangle formed by tangent to hyperbola $xy=c^2$ and its intercept is constant and equal to $2c^2.$
So, area of the triangle $=2(3{)}^2=18$sq. units.
Hence, the correct answer is option (c).