​The equation of the circle passing through the points of intersection of  the ellipse's x^2/a^2+y^2/b^2=1  and x^2/b^2+y^2/a^2=1 is-

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Please find below the solution to the asked query :
The required circle will be, x2a2+y2b2-1+λx2a2+y2b2-1= 0 x21a2+λb2+y21b2+λa2-1-λ=0 Now for circle, coefficient of x2 and y2 must be same so 1a2+λb2= 1b2+λa2λ1a2-1b2= 1a2-1b2λ= 1, putting this we get x21a2+1b2+y21b2+1a2-2=0 x2+y2= 21a2+1b2

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