# Find the equation to the straight line drawn at right angle to the straight line x/a-y/b=1 through the point where it meets x-axis?

Aug 6, 2018

Putting $y = 0$ in the given equation we get

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

$\implies \frac{x}{a} - \frac{0}{b} = 1$

$\implies x = a$

So the point of intersection of the line with the $x$-axis is $\left(a , 0\right)$

Equation of any straight line with the given one is $\frac{x}{b} + \frac{y}{a} + c = 0$ As it passes through $\left(a , 0\right)$ we have

$\frac{a}{b} + \frac{0}{a} + c = 0$

$\implies c = - \frac{a}{b}$

So equation of the required straight line

$\frac{x}{b} + \frac{y}{a} - \frac{a}{b} = 0$