Question

The area of the triangle formed by the tangents drawn to the points to a rectangular hyperbola $xy=16$ and its intercepts is $512$ sq. units. Identify these points.

• A. $(4,4)$
• B. $(-1,-16)$
• C. $(8,2)$
• D. $(2,8)$

Answer 1

Answer: (A), (B), (C), (D)

$(2,8)$

Area of triangle formed by tangent to hyperbola $xy=c^2$ and its intercept is CONSTANT and equal to $2c^2$.
Hence, it does not depend on the coordinates of the point on which tangent is drawn.