If $\quad a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ represents a pair of parallel lines, then $\sqrt{\frac{g^2-a…
If $\quad a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ represents a pair of parallel lines, then $\sqrt{\frac{g^2-a c}{f^2-b c}}$, is equal to
$\frac{a}{b}$
$\sqrt{\frac{a}{b}}$
$\sqrt{\frac{b}{a}}$
$\frac{b}{a}$
Solution
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, then
$\sqrt{\frac{g^2-a c}{a(a+b)}}=\sqrt{\frac{f^2-b c}{b(a+b)}}$
$\Rightarrow \quad \sqrt{\frac{g^2-a c}{f^2-b c}}=\sqrt{\frac{a}{b}}$