What is x^{(2)}+y^{(2)}-4x-6y+9=0 ?

The solution to x^{(2)}+y^{(2)}-4x-6y+9=0 is Circle with (a,b)=(2,3),r=2

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x^{(2)}+y^{(2)}-4x-6y+9=0

x^{(2)} + y^{(2)} - 4 x - 6 y + 9 = 0

(a, b) = (2, 3), r = 2

Solution steps

x^{2} + y^{2} - 4 x - 6 y + 9 = 0

Rewrite

x^{2} + y^{2} - 4 x - 6 y + 9 = 0

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (2, 3), r = 2

(x - 4)^{2} + (y + 3)^{2} = 16

x^{2} = 5 - y^{2}

y^{2} = - x^{2} + 5 x - 6

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

(x + 5)^{2} + (y - 8)^{2} = 121

What is x^{(2)}+y^{(2)}-4x-6y+9=0 ?
The solution to x^{(2)}+y^{(2)}-4x-6y+9=0 is Circle with (a,b)=(2,3),r=2