InterviewSolution
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InterviewSolution
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For the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2)) =1` and `(x^(2))/(b^(2))+(y^(2))/(a^(2)) =1`A. The foci of each ellipse always lie within the other ellipseB. Their auxiliary circles are the nameC. Their director circles are the sameD. The ellipses encloses the same area |
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Answer» Correct Answer - B::C::D Without loss of generality assume `a gt b` Foci of `1^(st)` ellipse are `(+- ae, 0)` Putting this point in `(x^(2))/(b^(2)) + (y^(2))/(a^(2)) -1`, we get `(a^(2)e^(2))/(b^(2)) -1` The above quantity may be negative or positive, hence option (a) is not correct Auxiliary circle for `(x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1` is `x^(2) + y^(2) =a^(2)` for `(x^(2))/(b^(2)) + (y^(2))/(a^(2)) =1` is `x^(2) + y^(2) =a^(2)` Director circle for `(x^(2))/(b^(2)) +(y^(2))/(a^(2)) =1` is `x^(2)+y^(2) = a^(2) +b^(2)` `(x^(2))/(b^(2)) +(y^(2))/(a^(2)) =1` is Area of the ellipse `= pi ab` |
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