Question

Find the equation of the straight line at a distance of 3 units from the origin such that the perpendicular from the origin to the line makes an angle tan⁻¹ \[\left( \frac{5}{12} \right)\] with the positive direction of x-axi .

Answer 1

Here, p = 3,

\[\alpha = \tan^{- 1} \left( \frac{5}{12} \right)\]

\[\therefore\text {  tan }\alpha = \frac{5}{12}\]

\[ \Rightarrow \text { sin} \alpha = \frac{5}{13} \text { and } cos\alpha = \frac{12}{13}\]

So, the equation of the line in normal form is

\[x\text { cos }\alpha + y\text { sin }\alpha = p\]

\[ \Rightarrow \frac{12x}{13} + \frac{5y}{13} = 3\]

\[ \Rightarrow 12x + 5y = 39\]