Explanation

(a)
$Given,\frac{1}{a}x^{2} + \frac{1}{b}y^{2} + 2\frac{1}{h}xy = 0$
$\therefore m_{1} + m_{2} = - \frac{\frac{2}{h}}{\frac{1}{b}} = \frac{- 2b}{h}\ \ldots(i)$
$and\ \ m_{1}m_{2} = \frac{\frac{1}{a}}{\frac{1}{b}} = \frac{b}{a}\ldots(ii)$
Also given $m_{2} = 2m_{1}$
$\Rightarrow 3m_{1} = \frac{- 2b}{h}\ \ \left\lbrack from\ Eq.(i) \right\rbrack\ldots.(iii)$
$and\ 2m_{1}^{2} = \frac{b}{a}\ \left\lbrack from\ Eq.(ii) \right\rbrack\ldots.(iv)$
From Eqs. (iii) and (iv),
$\frac{9m_{1}^{2}}{2m_{1}^{2}} = \frac{{4b}^{2}}{h^{2}} \times \frac{a}{b}$
$\Rightarrow \ \frac{9}{8} = \frac{ba}{h^{2}}\ or\ \ ab:h^{2} = 9:8$