The general form of the equation of a circle is:

(x - h)² + (y - k)² = r²

Where, (h, k) is the centre of the circle.

r is the radius of the circle.

Substituting the centre and radius of the circle in he general form:

⇒ (x - ( - a ))² + (y - ( - b))² = √(a²2 - b²2 )²

⇒ (x + a )² + (y + b)² = a² - b²

⇒ x² + 2xa + a² + y² + 2yα + b² = a² - b²

⇒ x² + 2xa + y² + 2yα = a² - 2b²

⇒ x² + y² + 2a(x + y) = a² - 2b²

⇒ x² + y² + 2a(x + y) = a² - 2b²

Ans; equation of a circle with Centre ( - a, - b) and radius

is:

⇒ x² + y² + 2a(x + y) = a² - 2b²