First slide

Pair of straight lines

Question

If $k x^{2} + 10 x y + 3 y^{2} - 15 x - 21 y + 18 = 0$ represents a pair of straight lines then k =

Moderate

Solution

$a = k, 2 h = 10, b = 3, 2 g = - 15$
$2 f = - 21, c = 18$
$a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0$
$k = 3$

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