If $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ represent parallel straight lines, then

h f = b g

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h^{2} = b c

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a^{2} f = b^{2} g

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None of these

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Solution

The correct option is A $h f = b g$
Given equation represents a pair of parallel straight lines, if $h^{2} = a b$ and $b g^{2} = a f^{2}$
$\Rightarrow h^{2} = \frac{b g^{2}}{f^{2}} b$
or $h^{2} f^{2} = b^{2} g^{2}$
So, $h f = b g$

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