Let $S$ be the circle in the $x y$-plane defined by the equation $x ^ { 2 } + y ^ { 2 } = 4$. 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 line segment $M N$ must lie on the curve (A) $( x + y ) ^ { 2 } = 3 x y$ (B) $x ^ { 2 / 3 } + y ^ { 2 / 3 } = 2 ^ { 4 / 3 }$ (C) $x ^ { 2 } + y ^ { 2 } = 2 x y$ (D) $x ^ { 2 } + y ^ { 2 } = x ^ { 2 } y ^ { 2 }$
Let $S$ be the circle in the $x y$-plane defined by the equation $x ^ { 2 } + y ^ { 2 } = 4$.\\
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 line segment $M N$ must lie on the curve\\
(A) $( x + y ) ^ { 2 } = 3 x y$\\
(B) $x ^ { 2 / 3 } + y ^ { 2 / 3 } = 2 ^ { 4 / 3 }$\\
(C) $x ^ { 2 } + y ^ { 2 } = 2 x y$\\
(D) $x ^ { 2 } + y ^ { 2 } = x ^ { 2 } y ^ { 2 }$