What is x^2+y^2=1+2y+y^2 ?

The solution to x^2+y^2=1+2y+y^2 is Parabola with (h,k)=(0,-1/2),p= 1/2

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x^2+y^2=1+2y+y^2

x^{2} + y^{2} = 1 + 2 y + y^{2}

(h, k) = (0, - \frac{1}{2}), p = \frac{1}{2}

Solution steps

x^{2} + y^{2} = 1 + 2 y + y^{2}

Rewrite

x^{2} + y^{2} - 1 - 2 y - y^{2} = 0

in the standard form

4 \cdot \frac{1}{2} (y - (- \frac{1}{2})) = (x - 0)^{2}

Therefore parabola properties are:

(h, k) = (0, - \frac{1}{2}), p = \frac{1}{2}

x^{2} y^{0} + 7 x y^{0} + 9 y = 0

y < 2 x^{2} - 2

x^{2} - 4 y - 12 x + 68 = 0

x^{2} - 8 x + 8 y + 16 = 0

y = x^{2} + 12 x + 16

What is x^2+y^2=1+2y+y^2 ?
The solution to x^2+y^2=1+2y+y^2 is Parabola with (h,k)=(0,-1/2),p= 1/2