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Tangents is d...

Question

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

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Solution

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

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