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

The solution to x^2=-y^2+2y is Ellipse with (h,k)=(0,1),a=1,b=1

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x^2=-y^2+2y

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

(h, k) = (0, 1), a = 1, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 1), a = 1, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 1, a = 1

(\frac{x - 3}{2})^{2} + y^{2} = \frac{9}{4}

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{49} = 1

4 x^{2} + 16 y^{2} - 16 x - 96 y + 96 = 0

17 x^{2} + 16 y^{2} - 102 x - 32 y - 103 = 0

x^{2} - 4 x + 100 y^{2} + 200 y + 4 = 0

What is x^2=-y^2+2y ?
The solution to x^2=-y^2+2y is Ellipse with (h,k)=(0,1),a=1,b=1