First slide

Pair of straight lines

Question

If the product of perpendiculars from (k, k) to the pair of lines $x^{2} + 4 x y + 3 y^{2} = 0$ is $4 / \sqrt{5}$ then k is

Moderate

A

$\pm 4$
B

$\pm 3$
C

$\pm 2$
D

$\pm 1$

Solution

$a = 1, 2 h = 4, b = 3$
$(α, β) = (k, k)$
$\frac{| a α^{2} + 2 h α β + b β^{2} |}{\sqrt{{(a - b)}^{2} + 4 h^{2}}} = \frac{4}{\sqrt{5}}$

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