The equation of the locus of points 5 units from the origin is
an equation of the locus of points 4 units from the point (2,-1) is
A point (x,y) is 5 units from the origin means that:
x^2 + y^2 = 25
which is the required equation of a circle centred at (0,0) of radius 5 units.
A point is 4 units from (2, -1) means that:an equation of the locus of points 4 units from the point (2,-1) is
(x-2)^2 + (y+1)^2 = 16
which is the required equation of a circle centred at (2,-1) of radius 4 units.
RonL