JEE Advanced 2011 Paper 1Question 1
A straight line $L$ through the point $(3,-2)$ is inclined at an angle $60^\circ$ to the line $\sqrt3x+y=1$. If $L$ also intersects the $x$-axis, then the equation of $L$ is
Points and Straight Lines
Solution
Given line has slope $-\sqrt3$ (inclination $120^\circ$). Lines at $60^\circ$ to it have inclination $60^\circ$ or $180^\circ$; the latter is horizontal and never meets the $x$-axis (excluded). So slope $\sqrt3$: $y+2=\sqrt3(x-3)$, i.e. $y-\sqrt3x+2+3\sqrt3=0$.