Question

Find the length of the perpendicular from the point $(a,b)$ to the line $\frac{x}{a}+\frac{y}{b}=1$.

Answer 1

Given equation of line is

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

We written that this equation

$bx+ay=ab$ …… (1)

We know that

Length of perpendicular any line $ax+by+c=0$

$d=\frac{ax+by+c}{\sqrt{a^2+b^2}}$

From equation (1),

$bx+ay-ab=0$

Length of perpendicular is

$d=\frac{bx+ay-ab}{\sqrt{b^2+a^2}}$

Length of perpendicular given point $(a,b)$

$d=\frac{b\times a+a\times b-ab}{\sqrt{b^2+a^2}}$

$d=\frac{ab}{\sqrt{a^2+b^2}}$

Hence it is required solution.