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

x^{2} + 4 y^{2} + 2 x - 12 y + 7 = 0

4 x^{2} - 8 x + 16 y^{2} - 96 y + 84 = 0

\frac{( x - 2 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{7} = 1

6 x^{2} - 6 x + 3 y^{2} + 3 y - 102 = 0

\frac{( x ^{2} )}{9} + \frac{( y ^{2} )}{4} = 1

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