Given that we need to find the equation of the circle with centre (a, a) and radius √2a.

We know that the equation of the circle with centre (p, q) and radius ‘r’ is given by:

⇒ (x - p)² + (y - q)² = r²

Now we substitute the corresponding values in the equation:

⇒ (x - a)² + (y - a)² = (a)²

⇒ x² - 2ax + a² + y² - 2ay + a² = 2a²

⇒ x² + y² - 2ax - 2ay = 0

∴The equation of the circle is x² + y² - 2ax - 2ay = 0.