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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

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a

x2+y2=a2

b

x2+y2=b2

c

x2+y2=a2b2a2+b2

d

x2+y2=2a2b2a2+b2

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detailed solution

Correct option is D

Given equations of ellipse arex2a2+y2b2=1 and x2b2+y2a2=1 The point of the intersection of these ellipse are±aba2+b2,±aba2+b2Paba2+b2,aba2+b2The distance between OP= r=aba2+b2−02+aba2+b2−02=aba2+b22∴ Equation of circle is x2+y4=r2⇒x2+y2=2a2b2a2+b2

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