The minimum area of a triangle formed by any tangent to the ellipse x²/16 + y²/81 = 1 and the coordinate axes is :

x²/16 + y²/81 = 1
The equation of a tangent can be written as : xcosθ/a + ysinθ/b = 1
The x intercept = acosθ
The y intercept = bsinθ
Δ = 1/2 × acosθ × bsinθ = (ab/2)sin2θ = 36sin2θ
Δ = 36sin2θ
Δ has maximum value of 18.