From \( (x-a)^2+(y-b)^2=r^2\) form, \(a=2,b=-1, r=3\)

From \( (x-a)^2+(y-b)^2=r^2\) form, \(a=-3,b=8, r=6\)

From \( (x-a)^2+(y-b)^2=r^2\) form, \(a=-5,b=-6, r=1\)

\( x^2 + y^2 - 6x + 8y + 10 = 0 \) Group \(x\) and \(y\) terms: \[ (x^2 - 6x) + (y^2 + 8y) = -10 \] Complete the square: \[ (x^2 - 6x + 9) + (y^2 + 8y + 16) = -10 + 9 + 16 \] \[ (x - 3)^2 + (y + 4)^2 = 15 \] \(\text{Centre: }(3,-4), \quad \text{Radius: }\sqrt{15}\)

Group terms: \[ (x^2 - x) + (y^2 - 10y) = -5 \] Complete the square: \[ (x^2 - x + \tfrac{1}{4}) + (y^2 - 10y + 25) = -5 + \tfrac{1}{4} + 25 \] \[ (x - \tfrac{1}{2})^2 + (y - 5)^2 = \tfrac{81}{4} \] \(\text{Centre: }(\tfrac{1}{2},\,5), \quad \text{Radius: }\tfrac{9}{2}\)

Divide by 2: \[ x^2 + y^2 - 4x + y + 1 = 0 \] Group terms: \[ (x^2 - 4x) + (y^2 + y) = -1 \] Complete the square: \[ (x^2 - 4x + 4) + (y^2 + y + \tfrac{1}{4}) = -1 + 4 + \tfrac{1}{4} \] \[ (x - 2)^2 + (y + \tfrac{1}{2})^2 = \tfrac{13}{4} \] \(\text{Centre: }(2,\,-\tfrac{1}{2}), \quad \text{Radius: }\tfrac{\sqrt{13}}{2}\)