Equation $12 x^{2} - 10 x y + 2 y^{2} + 11 x - 5 y + 2 = 0$ represent a pair of straight lines. Find the acute angle between them.

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Solution

The correct option is A

Given equation $12 x^{2} - 10 x y + 2 y^{2} + 11 x - 5 y + 2 = 0$

Comparing this equation by standard equation

$a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$

a = 12, h = -5, b = 2, g = $\frac{11}{2}$ ,f = $\frac{- 5}{2}$ , c = 2

acute angle between lines

$t a n θ = ∣ ∣ ∣ \frac{2 \sqrt{h^{2} - a b}}{a + b} ∣ ∣ ∣$

$t a n θ = \frac{2 \sqrt{25 - 24}}{14} |$

$t a n θ = \frac{2}{14} = \frac{1}{7}$

$t h e t a = t a n^{- 1} (\frac{1}{7})$

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Similar questions

x^{2} + λ x y + 2 y^{2} + 3 x - 5 y + 2 = 0

{tan}^{- 1} (\frac{1}{3})

^{'} λ^{'}

λ

λ

12 x^{2} - 10 x y + 2 y^{2} + 11 x - 5 y + λ = 0

The angle between the lines represented by the equation $4 x^{2} - 24 x y + 11 y^{2} = 0$ are

x^{2} - 3 x y + λ y^{2} + 3 x - 5 y + 2 = 0

{tan}^{- 1} (\frac{1}{3})

λ

λ

λ

12 x^{2} - 10 x y + 2 y^{2} + 11 x - 5 y + λ = 0

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