What is x^2+y^2-2y=0 ?

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

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x^2+y^2-2y=0

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

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

Solution steps

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

Rewrite

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

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

9 x^{2} - 9 y^{2} + 18 x + 36 y = 63

y^{2} = 28 x

\frac{x ^{2}}{64} - \frac{y ^{2}}{9} = 1

\frac{y ^{2}}{16} - \frac{x ^{2}}{25} = 1

\frac{x ^{2}}{64} - \frac{y ^{2}}{36} = 1

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