What is 2x^2+3x+2y^2+7y=52.75 ?

The solution to 2x^2+3x+2y^2+7y=52.75 is Circle with (a,b)=(-3/4 ,-7/4),r=sqrt(30)

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2x^2+3x+2y^2+7y=52.75

2 x^{2} + 3 x + 2 y^{2} + 7 y = 52.75

(a, b) = (- \frac{3}{4}, - \frac{7}{4}), r = 30

Solution steps

2 x^{2} + 3 x + 2 y^{2} + 7 y = 52.75

Rewrite

2 x^{2} + 3 x + 2 y^{2} + 7 y = 52.75

in the form of the standard circle equation

(x - (- \frac{3}{4}))^{2} + (y - (- \frac{7}{4}))^{2} = (30)^{2}

Therefore the circle properties are:

(a, b) = (- \frac{3}{4}, - \frac{7}{4}), r = 30

(x - 5)^{2} + (y - 2)^{2} = 49

(x - 15)^{2} + [y - (- 20)]^{2} = (9)^{2}

25 = (x + 7)^{2} + (y + 2)^{2}

x^{2} + y^{2} - 7 x + 2 y - 11 = 0

4 x^{2} + 4 y^{2} - 8 x + 32 y + 4 = 0

What is 2x^2+3x+2y^2+7y=52.75 ?
The solution to 2x^2+3x+2y^2+7y=52.75 is Circle with (a,b)=(-3/4 ,-7/4),r=sqrt(30)