Find the center and radius of each of the following circles

Find the center and radius of each of the following circles. (a) x^2 - 4x + y^2 + 2y - 15 = 0 center (x, y) = radius (b) x^2 + 2x + y^2 + 6y + 6 = 0 center (x, y) = radius (c) x^2 + 1/5x + y^2 - 18/5y = 41/3 (d) center (x, y) = radius (d) x^2 + y^2 = 3/2x - y + 19/16 center (x, y) = radius

Solution

x2-4x +y2 +2y -15 = 0 or, x2-4x +y2 +2y = 15 or, (x2-4x +4 )+( y2 +2y+1) = 15+4+1 or, (x-2)2+ (y+1)2 = 16. The center of this circle is (x,y) = (2,-1) and its radius is 4. x2 +2x +y2 +6y + 6 = 0 or, x2 +2x +y2 +6y = -6 or, (x2 +2x+1) + (y2 +6y+9)= -6+1+9 or, (x+1)2+(y+3)2 = 4. The center of this circle is (x,y) = (-1,-3) and its radius is 2. x2+x/5 + y2-18y/5 = 41/3 or, (x2+ 2*x*1/10 + 1/100) + (y2-2*y*9/5 +81/25) = 41/3+1/100+81/25 or, (x+1/10)2 +(y-9/5)2= 4427/300. The center of this circle is (x,y) = (-1/10,9/5) and its radius is (1/10)(4427/3). x2+y2 =3x/2-y +19/16 or, (x2-3x/2) +( y2+y) = 19/16 or, (x2-2*x*3/4 + 9/16) +( y2+2y +1)= 19/16 + 9/16+1 or, (x-3/4)2 +(y+1)2 = 11/4. The center of this circle is (x,y) = ( ¾,-1) and its radius is (1/2)11.