Question

Equation of the circle passing through the intersection of ellipses \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) and \(\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1\) is 

(A) x² + y² = a²

(B) x² + y² = b²

(C) x² + y² = \(\frac{a^2b^2}{a^2 + b^2}\)

(D) x² + y² = \(\frac{2a^2b^2}{a^2 + b^2}\)

Answer 1

Correct option is (D) x² + y² = \(\frac{2a^2b^2}{a^2 + b^2}\) 

Given equations of ellipse are

\(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) and \(\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1\)

The point of the intersection of these ellipse are

∴ Equation of circle is x² + y² = r²

⇒ x² + y² = \(\frac{2a^2b^2}{a^2 + b^2}\)