What is 4x^2+16x+15+4y^2+6y=0 ?

The solution to 4x^2+16x+15+4y^2+6y=0 is Circle with (a,b)=(-2,-3/4),r=(sqrt(13))/4

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4x^2+16x+15+4y^2+6y=0

4 x^{2} + 16 x + 15 + 4 y^{2} + 6 y = 0

(a, b) = (- 2, - \frac{3}{4}), r = \frac{13}{4}

Solution steps

4 x^{2} + 16 x + 15 + 4 y^{2} + 6 y = 0

Rewrite

4 x^{2} + 16 x + 15 + 4 y^{2} + 6 y = 0

in the form of the standard circle equation

(x - (- 2))^{2} + (y - (- \frac{3}{4}))^{2} = (\frac{13}{4})^{2}

Therefore the circle properties are:

(a, b) = (- 2, - \frac{3}{4}), r = \frac{13}{4}

x^{2} + y^{2} - 2 y - 8 x - 19 = 0

x^{2} - 4 x + y^{2} = 3 + 6 y

(x^{2} - 4 x) + (y^{2} - 6 y) = - 9

2 x^{2} + 2 y^{2} - 2 x + 2 y - 1 = 0

2 x^{2} + 2 y^{2} + 4 x + 12 y - 2 = 0

What is 4x^2+16x+15+4y^2+6y=0 ?
The solution to 4x^2+16x+15+4y^2+6y=0 is Circle with (a,b)=(-2,-3/4),r=(sqrt(13))/4