Question

focus (0, 12) directrix (y=-1/2)

Answer 1

Any idea?

Answer 2

Let (x,y) be any point on the locus.
If it is parabola then distance of (x,y) from focus=distance from directrix.
\[\sqrt{\left( y-12 \right)^2+\left( x-0 \right)^2}=\frac{ y+\frac{ 1 }{2 } }{ \sqrt{0^2+\left( 1 \right)^2} }\]
\[\left( y-12 \right)^2+x^2=\frac{ \left( y+\frac{ 1 }{ 2 } \right)^2 }{ 1 }\]
simplify it.