What is (x-5/2)^2+(y-1/2)^2= 169/4 ?

The solution to (x-5/2)^2+(y-1/2)^2= 169/4 is Circle with (a,b)=(5/2 , 1/2),r= 13/2

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(x-5/2)^2+(y-1/2)^2= 169/4

(x - \frac{5}{2})^{2} + (y - \frac{1}{2})^{2} = \frac{169}{4}

(a, b) = (\frac{5}{2}, \frac{1}{2}), r = \frac{13}{2}

Solution steps

(x - \frac{5}{2})^{2} + (y - \frac{1}{2})^{2} = \frac{169}{4}

Rewrite

(x - \frac{5}{2})^{2} + (y - \frac{1}{2})^{2} = \frac{169}{4}

in the form of the standard circle equation

(x - \frac{5}{2})^{2} + (y - \frac{1}{2})^{2} = (\frac{13}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{5}{2}, \frac{1}{2}), r = \frac{13}{2}

(x - 13)^{2} + (y + 13)^{2} = 16

x^{2} + 6 x + y^{2} - 2 y + 3 = 0

x^{2} + y^{2} - 18 x + 16 y + 120 = 0

x^{2} + y^{2} + 8 x - 12 y + 47 = 0

x^{2} + y^{2} - 3 x + 6 y + 9 = 0

What is (x-5/2)^2+(y-1/2)^2= 169/4 ?
The solution to (x-5/2)^2+(y-1/2)^2= 169/4 is Circle with (a,b)=(5/2 , 1/2),r= 13/2