The equation $9 x^{2} + 2 h x y + 4 y^{2} + 6 x + 2 f y + c = 0$ represents a pair of parallel straight lines $(h, f > 0)$ then

h < c < f

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c < f < h

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h < f < c

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c < h < f

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Solution

The correct option is B $c < f < h$
Given equation is $a x^{2} + b y^{2} + 2 h x y + 2 g x + 2 f y + c = 0$
Represent pair of parallel lines when
$h^{2} = a b, f^{2} \geq b c, g^{2} \geq a c, \frac{a}{h} = \frac{h}{b} = \frac{g}{f}, a f^{2} = b g^{2}$
Hence for $9 x^{2} + 4 y^{2} + 2 h x y + 6 x + 2 f y + c = 0$
$c < f < h$

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