What is (2x^2+6x+9)+(2y^2+2y+1)=45+9+1 ?

The solution to (2x^2+6x+9)+(2y^2+2y+1)=45+9+1 is Circle with (a,b)=(-3/2 ,-1/2),r=5

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(2x^2+6x+9)+(2y^2+2y+1)=45+9+1

(2 x^{2} + 6 x + 9) + (2 y^{2} + 2 y + 1) = 45 + 9 + 1

(a, b) = (- \frac{3}{2}, - \frac{1}{2}), r = 5

Solution steps

2 x^{2} + 6 x + 9 + (2 y^{2} + 2 y + 1) = 45 + 9 + 1

Rewrite

2 x^{2} + 6 x + 9 + (2 y^{2} + 2 y + 1) = 45 + 9 + 1

in the form of the standard circle equation

(x - (- \frac{3}{2}))^{2} + (y - (- \frac{1}{2}))^{2} = 5^{2}

Therefore the circle properties are:

(a, b) = (- \frac{3}{2}, - \frac{1}{2}), r = 5

4 x^{2} + 4 y^{2} - 16 x - 28 y + 41 = 0

y^{2} = - x^{2} + 196

(x + 7)^{2} + (y - 1)^{2} = 16

x^{2} + (y - 7)^{2} = 49

x^{2} + y^{2} - 2 x + 18 y + 81 = 0

What is (2x^2+6x+9)+(2y^2+2y+1)=45+9+1 ?
The solution to (2x^2+6x+9)+(2y^2+2y+1)=45+9+1 is Circle with (a,b)=(-3/2 ,-1/2),r=5