JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

Option A ($y^{2}=4 a x$) is correct because the distance from the point $(x,y)$ to $(a,0)$ being equal to its distance from the line $x+a=0$ leads to the equation $(x-a)^2 + y^2 = (x+a)^2$, which simplifies to $y^{2}=4 a x$.