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If the slope of one line is thrice the slope of another line and the equation of pair of lines is $\frac{x^{2}}{a} + \frac{2 xy}{h} + \frac{y^{2}}{b} = 0$ then $ab : h^{2}$ is

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5 : 3

2 : 3

1 : 3

4 : 3

answer is C.

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Detailed Solution

Let the slopes be m and 3m

$4 m = (- 2) \frac{b}{h} \Rightarrow m^{2} = \frac{b^{2}}{4 h^{2}}$

again $3 m^{2} = \frac{b}{a} \Rightarrow m^{2} = \frac{1}{3} \frac{b}{a}$

$∴ \frac{1}{4} \cdot \frac{b^{2}}{h^{2}} = \frac{1}{3} \frac{b}{a} \Rightarrow ab : h^{2} = 4 : 3$

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