How do I mark the locus of points $P$ for which $d (P, G) = d (P, L)$? Given is the area $G$ which is made up of the legs of the angle $A$. 
The line $L$ is parallel with one of the legs of angle $A$. 
How do I mark the locus of points $P$ for which 
$d (P, G) = d (P, L)$?
 A: Let the area (G) thus formed by the legs of angle A be a plane lying on a horizontal surface as shown below.
Draw a circle (of radius R) tangential to that plane. We have to imagine that the circle is now a vertical plane.
Any line (could be in the air) drawn parallel to AB (a leg of angle A) that is perpendicular to the circle plane and passing through the circumference of that circle qualifies as L [examples are L(1), L(2)….].
P(1), the center of this circle is one of the points that fits the description of d(P, G) = d(P, L) = R.
If we shift the circle to the right, then P(h), …, P(k),… all qualify. The locus we obtained so far is then the line in bold.
The whole setup can be visualized as rolling a cylinder on a piece of paper. Hope you can take it from here.
There are some more things need to be considered:-


*

*Can the bold line be extended infinitely to the right? And to the left?

*Can the cylindrical object be rolled infinitely to the ‘wall’? And toward you?

*What happens if R varies?

*This is only half of the solution. Where is the other half?

