Two straight lines $u=0\text{ and }V=0$ pass through the origin and the angle between them is ${\tan }^{-1}(7/9)$ If the ratio of the slope of $V=0\text{ and }u=0$ is 9/2, then their equations are

Let the slope of u = 0 be m. Then slope of v = 0 is 9m/2 . Therefore.$\frac{7}{9}=\left|\frac{m-\frac{9m}{2}}{1+m\times \frac{9m}{2}}\right|=\left|\frac{-7m}{2+9m^2}\right|$

$m=\frac{9\pm \sqrt{81-72}}{18}=\frac{9\pm 3}{18}=\frac{2}{3},\frac{1}{3}$

$\text{ or }m=\frac{-9\pm 3}{18}=-\frac{2}{3},-\frac{1}{3}$

Therefore, the equations of the lines are

$i) 3y = x and 2y = 3x ii) 3y = 2x and y = 3x$
$iii) x + 3y = 0 and 3x + 2y = 0$
$iv) 2x + 3y = 0 and 3x + y = 0$