If (a + 3b)(3a + b) = 4h2, then the angle between the lines represented by ax2

Question

If (a + 3b)(3a + b) = $4 h^{2}$ , then the angle between the lines represented by $a x^{2} + 2 h x y + b y^{2} = 0$ is

Options:

A .

90^{\circ}

B .

45^{\circ}

C .

60^{\circ}

D .

{tan}^{- 1} \frac{1}{2}

Answer: Option C
:
C

θ = t a n^{- 1} (\frac{2 \sqrt{h^{2} - a b}}{a + b}) = t a n^{- 1} (\frac{\sqrt{4 h^{2} - 4 a b}}{a + b})

= $t a n^{- 1} (\frac{\sqrt{3 a^{2} + 3 b^{2} + 10 a b - 4 a b}}{a + b}) = 60^{\circ}$ .

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