Let $\left(x_1, y_1\right)$ be any point other than origin on the parabola $y^2=16 a x$.
Then, length of subtangent at
$$
\begin{aligned}
\left(x_1, y_1\right)= & y_1\left(\frac{d x}{d y}\right)_{\left(x_1, y_1\right)} \\
\frac{d y}{d x}= & \frac{16 a}{2 y}=\frac{8 a}{y} \\
& {\left[\because y^2=16 a x \Rightarrow 2 y d y / d x=16 a\right] }
\end{aligned}
$$
Here,
$$
\begin{aligned}
\frac{d y}{d x}=\frac{16 a}{2 y} & =\frac{8 a}{y} \\
& {\left[\because y^2=16 a x \Rightarrow 2 y d y / d x=16 a\right] }
\end{aligned}
$$
$\therefore$ Length of subtangent at
$$
\left(x_1, y_1\right)=y_1\left(\frac{y_1}{8 a}\right)=\frac{y_1^2}{8 a}
$$
Now, the required ratio
$$
=\frac{\text { Length of subtangent at }\left(x_1, \mathrm{y}_1\right)}{x_1}=\frac{y_1^2}{\frac{8 a}{x_1}}
$$

$$
\begin{aligned}
& =\frac{y_1^2}{8 a} \times \frac{1}{x_1}=\frac{y_1^2}{8 a} \times \frac{16 a}{y_1^2} \\
& \\
& =\frac{2}{1} \quad\left[\because\left(x_1, y_1\right) \text { lies on } y^2=16 a x ; \therefore y_1^2=16 a x_1\right]
\end{aligned}
$$