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The angle through which the coordinates axes rotated so that xy-term in the equation $5 x^{2} + 4 \sqrt{3} x y + 9 y^{2} = 0$ may be missing, is

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Correct option is C

ln order to remove xy-term from the equationax2+2hxy+by2+2gx+2fy+c=0 the axes are rotate ofthrough an angle θ given bytan⁡2θ=2ha−bHere, a=5,b=9 and h=23∴ tan⁡2θ=2ha−b⇒ tan⁡2θ=435−9=−3⇒2θ=2π3⇒θ=π3

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The angle through which the coordinates axes rotated so that xy-term in the equation 5x2+43xy+9y2=0 may be missing, is

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The angle through which the coordinates axes rotated so that xy-term in the equation $5 x^{2} + 4 \sqrt{3} x y + 9 y^{2} = 0$ may be missing, is