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.

Question

PARAGRAPH “X”
Let S be the circle in the x-y 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 line segment MN must lie on the curve

(A) (x + y)² = 3xy (B) x^2/3 + y^2/3 = 2^4/3
(C) x² + y² = 2xy (D) x² + y² = x²y²

Answer 1

Answer:D

Solution: