I hope this helps you! This is just algebraic manipulation.
| \(x^2-9y^2=0\) | |
| \(x^2=9y^2\) | |
| \(\frac{x^2}{y^2}=9\) | |
| \(\left(\frac{x}{y}\right)^2=9\) | |
| \(\frac{x}{y}=\frac{3}{1}\\ x:y=3:1\) | Be careful! Do not take the negative root. "x" and "y" must both be positive. This is given information. |