Prove that the following equation represent pair of lines $9 x^{2} - 6 x y + y^{2} + 18 x - 6 y + 8 = 0$

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Solution

compare the equation with $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$
$a = 9$ , $b = 1$ , $h = - 3$
$h^{2} = 9$ , $a b = 9$
$h^{2} >= 9$
so this equation represents pair of straight lines and are parallel

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