Given that we need to find the equation of the circle whose end points of diameter are the foci of ellipse .

We know that foci of ellipse are (±ae,0).

We know that (0,0) is the centre of the ellipse and midpoint of the foci.

We know that distance between centre and any focus is ae.

So, we have with centre at (0,0) and radius ae.

We know that eccentricity of the ellipse

We know that the equation of the circle whose centre is (p,q) and radius ‘r’ is (x - p)² + (y - q)² = r²

⇒ (x - 0)² + (y - 0)² = (ae)²

⇒ x² + y² = a²e²

⇒

⇒ x² + y² = a² - b²

∴ The correct option is D