What is x^2+y^2-2sqrt(5)x=-1-3y ?

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

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x^2+y^2-2sqrt(5)x=-1-3y

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

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

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

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

(x - 11)^{2} + (y - 8)^{2} = 268

4 x^{2} - 24 x + 4 y^{2} + 20 y = 39

x^{2} + (y + 1)^{2} = 64

\frac{1}{2} x^{2} + \frac{1}{2} y^{2} = 1

(x^{2} - 2 x + 1) + (y^{2} - 4 y + 4) = 9

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