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
