JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

Option B ($x^{2}-3 y^{2}=0$) is correct because the distance from the point to the x-axis ($|y|$) is half its distance from the origin ($\sqrt{{x^2+y^2}}$), leading to the equation $|y| = \frac{{1}}{{2}} \sqrt{{x^2+y^2}}$, which simplifies to $x^{2}-3 y^{2}=0$.