First slide

Pair of straight lines

Question

The condition that the equation $a x^{2} + b y^{2} + c (x + y) = 0$ to represents a pair of straight lines is

Moderate

A

$a + b = 0 o r c = 0$
B

$a + b = 0 o r c = 0, a b < 0$
C

$a b > 0, c = 0$
D

$a + b \neq 0, c \neq 0$

Solution

$a = a, 2 h = 0, b = b, 2 g = c, 2 f = c, c = 0$
$a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0$
$a + b = 0 o r c = 0$
$h^{2} > a b a b < 0$

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