$\text{ The line }\frac{\mathrm{x}}{\mathrm{a}}-\frac{\mathrm{y}}{\mathrm{b}}=1\text{ meets the }\mathrm{x}\text{-axis at }\mathrm{P}\text{. Find }$the equation of line perpenducular to the line at P.

$$\begin{gathered} \mathrm{Given} line \frac{\mathrm{x}}{\mathrm{a}}-\frac{\mathrm{y}}{\mathrm{b}}=1 \\ \mathrm{bx}-\mathrm{ay}=\mathrm{ab}\dots \left(1\right) \end{gathered}$$
It meets the x-axis then  $\mathrm{y}=0$
$\text{ from }\left(1\right)\Rightarrow \mathrm{bx}=\mathrm{ab}\Rightarrow \mathrm{x}=a$
$\therefore \mathrm{P}=(a,0)$
Equation of line perpendicular to equation (1) and Passing through (a, 0) is ax + by + k = 0 .... (2)
$$\begin{gathered} sub(a,0) \\ \Rightarrow a\left(a\right)+0+\mathrm{k}=0 \\ \Rightarrow \mathrm{k}=-a^2 \end{gathered}$$
$\text{ from (2) }\mathrm{ax}+\mathrm{by}-a^2=0$