For the curve $y=c e^{x / a}$, which one of the following is incorrect?

equation of normal at the point where the curve cuts y-axis is $c y+a x=c$

We have,

$y=c e^{x / a} \Rightarrow \frac{d y}{d x}=\frac{c}{a} e^{x / a} \Rightarrow \frac{d y}{d x}=\frac{1}{a} y$

∴  $\frac{y}{d y / d x}$ = a = Const. ⇒ Subagent = Const.

Length of the subnormal

$=y \frac{d y}{d x}=y \times \frac{y}{a}=\frac{y^2}{a} \propto$ (Square of the ordinate)

Equation of the tangent at $\left(x_1, y_1\right)$ is

$y-y_1=\frac{y_1}{a}\left(x-x_1\right)$

This meets x-axis at a point given by

$-y=\frac{y_1}{a}\left(x-x_1\right) \Rightarrow x=x_1-a$

The curve meets y-axis at (0, c)

∴  $\left(\frac{d y}{d x}\right)_{(0, c)}=c / a$

So, equation of the normal at (0, c) is

$y-c=-\frac{1}{c / a}(x-0) \Rightarrow a x+c y=c^2$