Find the equation of the circle with:

Centre (a cos, a sin) and radius a.

Given that we need to find the equation of the circle with centre (acosα, asinα) and radius a.

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 - acosα)² + (y - asinα)² = a²

⇒ x² - (2acosα)x + a²cos²α + y² - (2asinα)y + a²sin²α = a²

We know that sin²θ + cos²θ = 1

⇒ x² - (2acosα)x + y² - 2asinαy + a² = a²

⇒ x² + y² - (2acosα)x - (2asinα)y = 0

∴The equation of the circle is x² + y² - (2acosα)x - (2asinα)y = 0.