What is (x-2)^2+(y-1)^2=42.25 ?

The solution to (x-2)^2+(y-1)^2=42.25 is Circle with (a,b)=(2,1),r=6.5

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(x-2)^2+(y-1)^2=42.25

(x - 2)^{2} + (y - 1)^{2} = 42.25

(a, b) = (2, 1), r = 6.5

Solution steps

(x - 2)^{2} + (y - 1)^{2} = 42.25

Rewrite

(x - 2)^{2} + (y - 1)^{2} = 42.25

in the form of the standard circle equation

(x - 2)^{2} + (y - 1)^{2} = 6. 5^{2}

Therefore the circle properties are:

(a, b) = (2, 1), r = 6.5

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

x^{2} + y^{2} - 8 x + 12 y + 48 = 0

x^{2} + y^{2} = 11 4^{2}

a^{2} + b^{2} = 40

a^{2} + b^{2} = 49

What is (x-2)^2+(y-1)^2=42.25 ?
The solution to (x-2)^2+(y-1)^2=42.25 is Circle with (a,b)=(2,1),r=6.5