The equation $y = \sqrt{2 - x^2 - y^2} + \sqrt{x^2 + y^2 - 2}$ represents, where $x > 0$

The given equation is:

$y=\sqrt{2-x^{2}-y^{2}}+\sqrt{x^{2}+y^{2}-2}$

We will analyze this equation step by step to determine what it represents.

Step 1: Analyze the domains of the square roots

For the square roots to be real, the expressions inside them must be non-negative:

1. $2-x^{2}-y^{2} \geq 0 \Longrightarrow x^{2}+y^{2} \leq 2$

2. $x^{2}+y^{2}-2 \geq 0 \Longrightarrow x^{2}+y^{2} \geq 2$

Combining these two conditions, we get:

$x^{2}+y^{2}=2$

This means the equation is only valid for points $(x, y)$ that lie on the circle $x^{2}+y^{2}=2$.

Circle with radius $2$ units