InterviewSolution
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InterviewSolution
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Find the equation of the ellipse whose centre is at origin, the distance between foci is 2 and eccentricity is `(1)/(sqrt(2))`. |
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Answer» Let the equation of the ellipse be `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and agtb`. Here `e=(1)/(sqrt(2))` and the distance between foci = 2ae = 2 `rArr" "ae=1` `rArr" "a((1)/(sqrt(2)))=1` `rArr""a=sqrt(2)` `rArr" "a^(2)=2` and `b^(2)=a^(2)(1-e^(2))` `=a^(2)-(a^(2)e^(2))=2-1=1` `:.` Equation of ellipse `(x^(2))/(2)+(y^(2))/(1)=1` `rArr" "x^(2)+2y^(2)=2`. |
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