If the slope of one line is double the slope of another line , and the combined equation of the pair of lines is $\frac{x^{2}}{a} + \frac{2 x y}{h} + \frac{y^{2}}{b} = 0,$ then $a b : h^{2}$ is equal to

9 : 8

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3 : 2

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8 : 3

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none of these

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Solution

The correct option is A $9 : 8$
Let assume slopes are $m$ and $2 m$
The equation in form of slope is $2 h m + b (m)^{2} = a$
So that
$m + 2 m = \frac{- 2 h}{b}$
and $m \times 2 m = \frac{a}{b}$
So simplify above equation and get
$\frac{h^{2}}{a b} = \frac{9}{8}$
Hence, option 'A' is correct.

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