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To remove $x y$ term from the second-degree equation $5 x^{2} + 8 x y + 5 y^{2} + 3 x + 2 y + 5 = 0$ the coordinate axes are rotated through an angle $θ,$ then $θ$ is

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$\frac{3 π}{8}$

$\frac{π}{4}$

$\frac{π}{8}$

$\frac{π}{2}$

answer is B.

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Detailed Solution

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

If $a = b \Rightarrow θ = \frac{π}{4}$

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