The area common to the ellipses \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) and \(\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1\), 0 < b < a is
A. \((a+b)^{2} \tan ^{-1} \frac{b}{a}\)
B. \((a+b)^{2} \tan ^{-1} \frac{a}{b}\)
C. \(4 a b \tan ^{-1} \frac{b}{a}\)
D. \(4 a b \tan ^{-1} \frac{a}{b}\)
Answer:C
The area common to the ellipses \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) and \(\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1\), 0 < b < a is
A. \((a+b)^{2} \tan ^{-1} \frac{b}{a}\) B. \((a+b)^{2} \tan ^{-1} \frac{a}{b}\) C. \(4 a b \tan ^{-1} \frac{b}{a}\) D. \(4 a b \tan ^{-1} \frac{a}{b}\)