What is x^2=-y^2+10y+5 ?

The solution to x^2=-y^2+10y+5 is Circle with (a,b)=(0,5),r=sqrt(30)

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x^2=-y^2+10y+5

x^{2} = - y^{2} + 10 y + 5

(a, b) = (0, 5), r = 30

Solution steps

x^{2} = - y^{2} + 10 y + 5

Rewrite

x^{2} = - y^{2} + 10 y + 5

in the form of the standard circle equation

(x - 0)^{2} + (y - 5)^{2} = (30)^{2}

Therefore the circle properties are:

(a, b) = (0, 5), r = 30

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

(x - 12)^{2} + y^{2} = 144

(2 x^{2} + 6 x + 9) + (2 y^{2} + 2 y + 1) = 45 + 9 + 1

4 x^{2} + 4 y^{2} - 16 x - 28 y + 41 = 0

y^{2} = - x^{2} + 196

What is x^2=-y^2+10y+5 ?
The solution to x^2=-y^2+10y+5 is Circle with (a,b)=(0,5),r=sqrt(30)