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

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

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

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

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

Solution steps

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

Rewrite

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

in the standard form

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

Therefore parabola properties are:

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

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

y - x^{2} = - 4

(x - h)^{2} = - 4 a (y - k)

y^{2} = 12 (x - 4)

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

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