What is locus and equation of the locus of point ?

what is a locus

Define locus of a point .

(1) The equation of locus of the point whose the distance from the x -axis is twice that of from the y -axis is (2) The equation of the locus of the point which moves equidistant form the coordinate axes is

If A(1,3) and B(2,1) are points,find the equation of the locus of point P such that PA=PB

If A(2,0) and B(0,3) are two points,find the equation of the locus of point P such thatt AP=2BP .

If O is origin and R is a variable point on y^(2)=4x , then find the equation of the locus of the mid-point of the line segment OR.

If O is origin and R is a variable point on y^2=4x , then find the equation of the locus of the mid-point of the line segmet OR .