I\'m having some trouble with these circle equation problemsand would like some

Question

I'm having some trouble with these circle equation problemsand would like some help. Thanks! Rewrite each equation in Standard form. State the center andthe radius. x^2 + y^2 +30x = 0 x^2 + y^2 - y - 2 = 0 x^2 + y^2 + 4x - 4y = 0 x^2 + y^2 + 2x + 4y = 0 3x^2 + 3y^2 - 18x + 24y - 33 = 0 x^2 + y^2 - 5x - 7y - 3 = 0 5x^2 + 5y^2 + 12x - 6y - 1 = 0 I'm having some trouble with these circle equation problemsand would like some help. Thanks! Rewrite each equation in Standard form. State the center andthe radius. x^2 + y^2 +30x = 0 x^2 + y^2 - y - 2 = 0 x^2 + y^2 + 4x - 4y = 0 x^2 + y^2 + 2x + 4y = 0 3x^2 + 3y^2 - 18x + 24y - 33 = 0 x^2 + y^2 - 5x - 7y - 3 = 0 5x^2 + 5y^2 + 12x - 6y - 1 = 0

Explanation / Answer

x2 + 30x + y^2 = 0 x^2 + 30x + 225 - 225 + y^2 = 0 (x+15)^2 + y^2 = 225 Center: (-15, 0) Radius = 225 =15 ... x^2 + y^2 - y - 2 = 0 x^2 + y^2 - y +1/4 - 1/4 - 2 = 0 x^2 + (y-1/2)^2 - 1/4 - 2 = x^2 + (y-1/2)^2 = 9/4 Ceneter: (0, 1/2) Radius = (9/4) =3/2 ... x^2 + y^2 + 4x - 4y = 0 x^2 + 4x + 4 - 4 + y^2 - 4y +4 - 4= 0 (x+2)^2 - 4 + (y-2)^2 - 4 = 0 (x+2)^2 + (y-2)^2 = 8 Center (-2, 2) Radius = 8 ... x^2 + y^2 + 2x + 4y = 0 x^2 + 2x + 1 - 1 + y^2 + 4y + 4 - 4 = 0 (x+1)^2 - 1 + (y+2)^2 - 4 = 0 (x+1)^2 + (y+2)^2 = 5 Center (-1, -2) Radius = 5 ... x^2 + y^2 - 5x - 7y - 3 = 0 x^2 - 5x + 25/4 - 25/4 + y^2 - 7y + 49/2 - 49/2 -3 = 0 (x-5/2)^2 + (y-7/2)^2 = 25/4 + 49/4 + 3 = 74/4 + 12/4 = 86 /4 Center (5/2, 7/2) Radius = (86/4) = (86)/ 2 ... x^2 + y^2 - 5x - 7y - 3 = 0 x^2 - 5x + 25/4 - 25/4 + y^2 - 7y + 49/2 - 49/2 -3 = 0 (x-5/2)^2 + (y-7/2)^2 = 25/4 + 49/4 + 3 = 74/4 + 12/4 = 86 /4 Center (5/2, 7/2) Radius = (86/4) = (86)/ 2

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