The given equation of circle is, x2+y2 – 8x + 10y – 12 = 0
∴ (x2–8x)+(y2+10y) = 12
⇒ [x2 – 8x + (4)2] + [y2 + 10y + (5)2] = 12 + (4)2+(5)2
⇒ (x–4)2+(y+5)2 = 12 + 16 + 25 ⇒ (x–4)2+(y+5)2 = 53
⇒ (x–4)2+(y+5)2 = (√53)2
Comparing it with (x–h)2+(y–k)2 = r2, we have h = 4, k = –5 and r = √53.
Thus co-ordinates of the centre are (4, –5) and radius is √53.