I am studying analytical geometry where i encountered the below problem.I searched the concept on the MSE site but found that question on the topic are poorly framed.
We are given the equations of the following three lines in general form. $$L_1:u_1=0,v_1=0$$ $$L_2:u_2=0,v_2=0$$ $$L_3:u_3=0,v_3=0$$ We need to find the locus of a straight line intersecting these lines .In my understanding , a locus is the path traced by a point subject to some conditions . I have never heard of locus of something called the straight line.Therefore ,I have following questions :-
- Can someone interpret what is the intuitive / physical meaning of locus of a straight line . Does it mean in this example ,all the lines that intersect the given three lines form some kind of surface in 3-D space ? Can we extend this definition therefore to locus of a circle , locus of an ellipse , locus of hyperbola etc.
- If the above question can be solved using the definition ?