What is 5x^2+5y^2+10x-5y+3=0 ?

The solution to 5x^2+5y^2+10x-5y+3=0 is Circle with (a,b)=(-1, 1/2),r=(sqrt(13))/(2sqrt(5))

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5x^2+5y^2+10x-5y+3=0

5 x^{2} + 5 y^{2} + 10 x - 5 y + 3 = 0

(a, b) = (- 1, \frac{1}{2}), r = \frac{13}{2 5}

Solution steps

5 x^{2} + 5 y^{2} + 10 x - 5 y + 3 = 0

Rewrite

5 x^{2} + 5 y^{2} + 10 x - 5 y + 3 = 0

in the form of the standard circle equation

(x - (- 1))^{2} + (y - \frac{1}{2})^{2} = (\frac{13}{2 5})^{2}

Therefore the circle properties are:

(a, b) = (- 1, \frac{1}{2}), r = \frac{13}{2 5}

(x - 1)^{2} + (y + 3)^{2} = 25

x^{2} + (y - 4)^{2} = 1

y^{2} = 16 - x^{2}

x^{2} + y^{2} - 8 = 0

25 x^{2} + 25 y^{2} + 30 x - 20 y - 62 = 0

What is 5x^2+5y^2+10x-5y+3=0 ?
The solution to 5x^2+5y^2+10x-5y+3=0 is Circle with (a,b)=(-1, 1/2),r=(sqrt(13))/(2sqrt(5))