JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

Option B ($y^{2}-2 a x+a^{2}=0$) is correct because the distance from the point $(x,y)$ to $(a,0)$ being equal to its distance from the y-axis ($x=0$) leads to the equation $(x-a)^2 + y^2 = x^2$, which simplifies to $y^{2}-2 a x+a^{2}=0$.