Question 1056673
Line is point (x,2) and other line is  point (-1,y).


General point  (x,y) is same distance from both those lines, using Distance Formula:
{{{sqrt((x-x)^2+(y-2)^2)=sqrt((x-(-1))^2+(y-y)^2)}}}
Simplify this, and that gives your locus of points asked.


{{{(y-2)^2=(x+1)^2}}}