Let S be the circle in the xy-plane defined by the equation x² + y² = 4. Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the segment MN must lie on the curve.

Given equation of circle is x² + y² = 4
Equation of tangent to S is given by xx₁/4 + yy₁/4 = 1.. (i)
which is same as x²/h + y²/k = 1.. (ii)
Tangent at P(2cosθ, 2sinθ) is xcosθ + ysinθ = 2 ⇒ M(2secθ, 0) and N(0, 2cosecθ) from (i) and (ii)
Midpoint is (h, k) ⇒ h = secθ, k = cosecθ ⇒ 1/h² + 1/k² = 1 ⇒ 1/x² + 1/y² = 1 ⇒ x² + y² = x²y².