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

The solution to x^2+2y+1=2+x^2-y is Parabola with (h,k)=(0, 1/3),p= 1/4

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

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

(h, k) = (0, \frac{1}{3}), p = \frac{1}{4}

Solution steps

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

Rewrite

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

in the standard form

4 \cdot \frac{1}{4} (y - \frac{1}{3}) = (x - 0)^{2}

Therefore parabola properties are:

(h, k) = (0, \frac{1}{3}), p = \frac{1}{4}

x^{2} - 6 x - y + 17 = 0

(x + 2)^{2} = 8 (y - 1)

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

y^{2} + 6 y - 2 x + 13 = 0

x^{2} - 10 x - 24 y = - 25 - 24

What is x^2+2y+1=2+x^2-y ?
The solution to x^2+2y+1=2+x^2-y is Parabola with (h,k)=(0, 1/3),p= 1/4