(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.