Question

Find the joint equation of the passing through the origin having the inclinations ${30}^o$ and ${120}^o$

• A. $y^2-\frac{x^2}{3}=0$
• B. $y^2+\frac{x^2}{3}=0$
• C. $y^2-\frac{{2x}^2}{3}=0$
• D. $y^2+\frac{{2x}^2}{3}=0$

Answer 1

The correct option is A $y^2-\frac{x^2}{3}=0$

Equation of line passing through the origin is of form $y=mx$

So the lines are

$y=x\tan {30}^{o}y=\frac{x}{\sqrt{3}}y-\frac{x}{\sqrt{3}}=0y=x\tan {120}^{o}y=-\frac{x}{\sqrt{3}}y+\frac{x}{\sqrt{3}}=0$

$y^2-\frac{x^2}{3}=0$