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The angle of rotation of axes to remove the xy term
List – I List – II
(A) $9 x^{2} + 2 \sqrt{3} x y + 7 y^{2} = 0$ (I) $\frac{π}{12}$
(B) $7 x^{2} + 2 \sqrt{3} x y + 5 y^{2} = 0$ (II) $\frac{π}{4}$
(C) $3 x^{2} + 2 x y + y^{2} = 2$ (III) $\frac{π}{3}$
(D) $3 x^{2} - 2 \sqrt{3} x y + 9 y^{2} = 10$ (IV) $\frac{π}{6}$
(V) $\frac{π}{8}$
The correct matching is

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$A - I V, B - I V, C - V, D - I$

$A - I I I, B - I I I, C - V, D - I I$

$A - I I I, B - I, C - V, D - I V$

$A - I V, B - I, C - I I, D - I I$

answer is A.

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$θ = \frac{1}{2} \tan^{- 1} (\frac{2 h}{a - b})$

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