What is 4x^2+24x+4y^2-20y=-45 ?

The solution to 4x^2+24x+4y^2-20y=-45 is Circle with (a,b)=(-3, 5/2),r=2

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4x^2+24x+4y^2-20y=-45

4 x^{2} + 24 x + 4 y^{2} - 20 y = - 45

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

Solution steps

4 x^{2} + 24 x + 4 y^{2} - 20 y = - 45

Rewrite

4 x^{2} + 24 x + 4 y^{2} - 20 y = - 45

in the form of the standard circle equation

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

Therefore the circle properties are:

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

(x - 20)^{2} + (y - 24)^{2} = 625

(x + 3)^{2} + (y - 5)^{2} = 85

(x - 5.5)^{2} + (y - 0.5)^{2} = 3.53

x^{2} + y^{2} - 20 x - 10 y = 5925

x^{2} - 1 x + y^{2} - 3 y - 20 = 0

What is 4x^2+24x+4y^2-20y=-45 ?
The solution to 4x^2+24x+4y^2-20y=-45 is Circle with (a,b)=(-3, 5/2),r=2