The joint equation of two lines through the origin, each making an angle with measure of $30^{\circ}$ with…
The joint equation of two lines through the origin, each making an angle with measure of $30^{\circ}$ with the positive Y -axis, is
$\quad x^2-3 y^2=0$
$2 x^2-3 y^2=0$
$3 x^2-y^2=0$
$x^2+3 y^2=0$
Solution
Slopes of the required lines are $\mathrm{m}_1=\sqrt{3}$, $\mathrm{m}_2=-\sqrt{3}$
$\therefore \quad$ Required lines are $(y-\sqrt{3} x)(y+\sqrt{3} x)=0$ $\Rightarrow 3 x^2-y^2=0$