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 - 0)² + (y - 0)² = 4²

⇒ x² + y² = 16

Ans; equation of a circle with . Centre at the origin and radius 4 is:

x² + y² = 16