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 $\alpha$ given by $ta{n}^{-1}\left(\frac{5}{12}\right)$ with the positive direction of x-axis.

Answer 1

$\text{Here}p=3$

$and\alpha =ta{n}^{-1}\left(\frac{5}{12}\right)$

$\Rightarrow cos\alpha =\frac{12}{13},sin\alpha =\frac{5}{13}$

$\text{Equation of straight line is :}$

$xcos\alpha +ysin\alpha =p$

$x\left(\frac{12}{13}\right)+y\left(\frac{5}{13}\right)=3$

$12x+5y=39$