What is 3x^2+3y^2-12x+15y-21=0 ?

The solution to 3x^2+3y^2-12x+15y-21=0 is Circle with (a,b)=(2,-5/2),r=(sqrt(69))/2

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3x^2+3y^2-12x+15y-21=0

3 x^{2} + 3 y^{2} - 12 x + 15 y - 21 = 0

(a, b) = (2, - \frac{5}{2}), r = \frac{69}{2}

Solution steps

3 x^{2} + 3 y^{2} - 12 x + 15 y - 21 = 0

Rewrite

3 x^{2} + 3 y^{2} - 12 x + 15 y - 21 = 0

in the form of the standard circle equation

(x - 2)^{2} + (y - (- \frac{5}{2}))^{2} = (\frac{69}{2})^{2}

Therefore the circle properties are:

(a, b) = (2, - \frac{5}{2}), r = \frac{69}{2}

(x + 1)^{2} + y^{2} = 16

x^{2} + y^{2} - 14 x - 8 y + 65 = 25

x^{2} + 16 x + 64 + y^{2} - 2 y + 1 = 144

(x + 5)^{2} + y^{2} = 25

What is 3x^2+3y^2-12x+15y-21=0 ?
The solution to 3x^2+3y^2-12x+15y-21=0 is Circle with (a,b)=(2,-5/2),r=(sqrt(69))/2