(i) Given that we need to find the equation of the circle with centre ( - 2, 3) and radius 4.
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 - ( - 2))2 + (y - 3)2 = 42
⇒ (x + 2)2 + (y - 3)2 = 16
⇒ x2 + 4x + 4 + y2 - 6y + 9 = 16
⇒ x2 + y2 + 4x - 6y - 3 = 0
∴The equation of the circle is x2 + y2 + 4x - 6y - 3 = 0.