This is the concept of algebra, the equation seen is an equation of the circle, and to solve it we proceed as follows;
the general form of the equation of the circle is:
(x-a)^2+(y-b)^2=r^2
where:
(a,b) is the center of the circle
r=radius:
x^2+y^2-8x+10y+10=0
this can v=be re-written as follows;
x^2-8x+y^2+10y=-10.......i
but:
c=(b/2)^2
c=(-8/2)^2=16
also:
c=(10/2)^2=25
hence substituting the above values in [i] we get:
x^2-8x+16+y^2+10y+25=-10+16+25
this can be written as:
(x-4)^2+(y+5)^2=31
therefore our equation is the equation of the circle with center (4,-5) and radius r=sqrt 31: