Question

Find the equation to the straight line drawn at right angles to the straight line $\frac{x}{a}-\frac{y}{b}=1$ through the point where it meets the axis $a$ of $x$

Answer 1

Given line is $\frac{x}{a}-\frac{y}{b}=1$

Slope is $m=\frac{b}{a}$

Then perpendicular slope is $m_1=\frac{-a}{b}$

Then the equation of the line with this slope is $y=\frac{-a}{b}x+c$.......$\left(1\right)$

As $(a,0)$ passes through the above line (Given line meets at $x-axis$ i.e., put $y=0$)

Then, $0=\frac{-a}{b}\times a+c$

$\Rightarrow c=\frac{a^2}{b}$

Therefore required line is $by+ax=a^2$ (Substitute ${}^{\prime }{c}^{\prime }$ in $\left(1\right)$ and simplify)