First slide

Pair of straight lines

Question

If the angle between the pair of lines $2 x^{2} + λ x y + 3 y^{2} + 8 x + 14 y + 8 = 0$ is $\frac{π}{4}$ , then the value of $| λ |$ is

Moderate

Solution

$a = 2, 2 h = λ, b = 3$ ; $2 g = 8, 2 f = 14, c = 8$
$\cos θ = \frac{| a + b |}{\sqrt{{(a - b)}^{2} + 4 h^{2}}}$

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