Find the length of the perpendicular drawn from
the point $(b, a)$ upon the straight line $\frac{x}{a} - \frac{y}{b} = 1$

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Solution

$b x - a y = a b$
Perpendicular distance is = $∣ ∣ ∣ \frac{b x - a y - a b}{\sqrt{a^{2} + b^{2}}} ∣ ∣ ∣$
Given point is $(b, a)$
Therefore perpendicular distance = $∣ ∣ ∣ \frac{b \times b - a \times a - a b}{\sqrt{a^{2} + b^{2}}} ∣ ∣ ∣$
$\Rightarrow ∣ ∣ ∣ \frac{b^{2} - a^{2} - a b}{\sqrt{a^{2} + b^{2}}} ∣ ∣ ∣$

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