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The minimum distance of any point on the ellipse $x^{2} + 3 y^{2} + 4 x y = 4$ from its centre is

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25−2

25+2

22−1

22+1

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detailed solution

Correct option is A

Let any point on the ellipse be rcosθ,rsinθ⇒ d2=4cos2θ+3sin2θ+2sin2θ-81+cos2θ+3-3cos2θ+4sin2θ =42sin2θ−cos2θ+2 Hence Emin=25-2

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The minimum distance of any point on the ellipse x2+3y2+4xy=4 from its centre is

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The minimum distance of any point on the ellipse $x^{2} + 3 y^{2} + 4 x y = 4$ from its centre is