If pair of lines represented by $a x^{2} + 2 h x y + b y^{2} = 0$ , $b \neq 0$ , are such that the sum of the slopes of the lines is three times the product of their slopes, then

3 b + 2 h = 0

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3 a + 2 h = 0

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3 h + 2 a = 0

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none of these

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Solution

The correct option is B $3 a + 2 h = 0$
Let assume slopes are $m_{1}$ and $m_{2}$
$m_{1} + m_{2} = 3 \times m_{1} m_{2}$
the equation in form of slope is $2 h m + b (m)^{2} + a = 0$
so that
$m_{1} + m_{2} = \frac{- 2 h}{b}$
and $m_{1} m_{2} = \frac{a}{b}$
So $\frac{- 2 h}{b} = \frac{3 a}{b}$
$3 a + 2 h = 0$
Hence, option 'B' is correct.

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