If the pair of straight lines $a x^{2} + 2 h x y - a y^{2} = 0$ and $b x^{2} + 2 g x y - b y^{2} = 0$ be such that each bisect the angle between the other, then

h g + a b = 0

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a h + b g = 0

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h^{2} - a b = 0

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a g - b h = 0

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Solution

The correct option is A $h g + a b = 0$
The equation of bisectors of $a x^{2} + 2 h x y - a y^{2}$ is
$\frac{x^{2} - y^{2}}{a - (- a)} = \frac{x y}{h}$

$h x^{2} - 2 a x y - h y^{2} = 0$ .................(1)

and, $b x^{2} + 2 g x y - b y^{2} = 0$ ....................(2)
comparing both the equations:

$\frac{h}{b} = \frac{- 2 a}{2 g}$

$h g = - a b$

$h g + a b = 0$

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