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 cos ∝))² + (y - (a sin ∝))² = a²

⇒ (x - a cos ∝)² + (y - a sin ∝)² = a²

⇒ x² - 2xacos α + a² cos² α + y² - 2yasin α + a² sin² α = a²

⇒ x² + y² + a² (cos² α + sin² α) - 2a(xcos α + ysin α) = a²

⇒ x² + y² + a² - 2a(xcos α + ysin α) = a² …((cos²α + sin² α) = 1)

⇒ x² + y² - 2a(xcos α + ysin α) = 0

Ans: equation of a circle with Centre (a cos ∝, a sin ∝) and radius a is:

x² + y² - 2a(xcos α + ysin α) = 0