What are the center and radius of the circle defined by the equation ?
x^2-y^2-6x+10y+25=0

The given equation represents a circle with center at (3,−5) and radius 3.

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.