The given equation represents a circle with center at (3,−5) and radius 3.
Explanation:
x2+y2−6x+10y+25=0 can be written as
x2−6x+y2+10y+25=0 or
x2−6x+9+y2+10y+25=9 or
(x−3)2+(y+5)2=32 or
(x−3)2+(y−(−5))2=32
This is the locus of a point which moves so that it moves at constant distance of 3 from the point (3,−5).
Hence the given equation represents a circle with center at (3,−5) and radius 3.
