The length of the perpendicular from origin to the line $12 x - 5 y = 4$ is

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$\frac{4}{13}$

$\frac{13}{2}$

$\frac{13}{4}$

$\frac{2}{13}$

answer is A.

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Detailed Solution

$\begin{array}{l} 12 x - 5 y = 4 \\ \Rightarrow \frac{12 x}{\sqrt{12^{2} + 5^{2}}} - \frac{5 y}{\sqrt{12^{2} + 5^{2}}} = \frac{4}{\sqrt{12^{2} + 5^{2}}} \\ \Rightarrow \frac{12 x}{13} - \frac{5 y}{13} = \frac{4}{13} \end{array}$

Compare with $x \cos α + y \sin α = p$

$∴ p = \frac{4}{13}$

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