Equation of a Circle

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  1. B.  $(x-3)^2+y^2=25$
  2. D.  $x^2+(y+2)^2=4$
  3. C. 4            $\eqalign{\\x^2+y^2-2x+6y=6\\x^2-2x+\text{___}+y^2+6y+\text{___}=6\\x^2-2x+\mathbf{1}+y^2+6y+\mathbf{9}=6+1+9\\(x-1)^2+(y+3)^2=16\\r^2=16\\r=4\\\\}$
  4. C. 7            $\eqalign{\\x^2+y^2+12x-10y=-12\\x^2+12x+\text{___}+y^2-10y+\text{___}=-12\\x^2+12x+\mathbf{36}+y^2-10y+\mathbf{25}=-12+36+25\\(x+6)^2+(y-5)^2=49\\r^2=49\\r=7\\\\}$
  5. C. (4,-1)     $\eqalign{\\x^2+y^2-8x+2y=-4\\x^2-8x+\text{___}+y^2+2y+\text{___}=-4\\x^2-8x+\mathbf{16}+y^2+2y+\mathbf{1}=-4+16+1\\(x-4)^2+(y+1)^2=-4+16+1\\(x-4)^2+(y+1)^2=13\\(h,k)=(4, -1)\\\\}$
  6. A. (1.5, 2.5)  $\eqalign{\\x^2+y^2-3x-5y=-10\\x^2-3x+\text{___}+y^2-5y+\text{___}=-10\\x^2-3x+\mathbf{2.25}+y^2-5y+\mathbf{6.25}=-3+2.25+6.25\\(x-1.5)^2+(y-2.5)^2=5.5\\(h,k)=(1.5, 2.5)}$