1.

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.

Answer»

`(X+y)^(2) = 3XY`
`x^(2//3) + y^(2//3) = 2^(4//3)`
`x^(2) + y^(2) = 2XY`
`x^(2) + y^(2) = x^(2)y^(2)`

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