First slide

Pair of straight lines

Question

If $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ represents a pair of parallel lines the $\sqrt{\frac{g^{2} - a c}{f^{2} - b c}} =$

Moderate

A

$\frac{a}{b}$
B

$\sqrt{\frac{a}{b}}$
C

$\sqrt{\frac{b}{a}}$
D

$\frac{b}{a}$

Solution

$2 \sqrt{\frac{g^{2} - a c}{a (a + b)}} = 2 \sqrt{\frac{f^{2} - b c}{b (a + b)}}$
$\frac{\sqrt{g^{2} - a c}}{\sqrt{a}} = \frac{\sqrt{f^{2} - b c}}{\sqrt{b}}$

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