What is x^2+y^2+42x+84y+65=0 ?

The solution to x^2+y^2+42x+84y+65=0 is Circle with (a,b)=(-21,-42),r=2sqrt(535)

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x^2+y^2+42x+84y+65=0

x^{2} + y^{2} + 42 x + 84 y + 65 = 0

(a, b) = (- 21, - 42), r = 2535

Solution steps

x^{2} + y^{2} + 42 x + 84 y + 65 = 0

Rewrite

x^{2} + y^{2} + 42 x + 84 y + 65 = 0

in the form of the standard circle equation

(x - (- 21))^{2} + (y - (- 42))^{2} = (2535)^{2}

Therefore the circle properties are:

(a, b) = (- 21, - 42), r = 2535

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

x^{2} - 14 x + y^{2} + 12 y = 36

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

9 - x^{2} - y^{2} > 0

x^{2} + x + y^{2} + 11 y - 32 = 0

What is x^2+y^2+42x+84y+65=0 ?
The solution to x^2+y^2+42x+84y+65=0 is Circle with (a,b)=(-21,-42),r=2sqrt(535)