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The condition that one of the pair of lines $a x^{2} + 2 h x y + b y^{2} = 0$ be coincident with one line of the pair $3 x^{2} + 12 x y + 2 y^{2} = 0$ and the remaining lines are at right angles, then h (a-b) =

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a+b

2ab

$\frac{a}{b}$

answer is B.

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Detailed Solution

$a_{1} = a, 2 h_{1} = 2 h, b_{1} = b$

$a_{2} = 3, 2 h_{2} = 12, b_{2} = 2$

$\frac{h_{1} a_{2} b_{2}}{b_{2} - a_{2}} = \frac{h_{2} a_{1} b_{1}}{b_{1} - a_{1}}$

$\Rightarrow \frac{h (3) (2)}{2 - 3} = \frac{6 (a) (b)}{b - a} \Rightarrow h (a - b) = a b$

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