What is y^2+x^2-4y=0 ?

The solution to y^2+x^2-4y=0 is Ellipse with (h,k)=(0,2),a=2,b=2

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y^2+x^2-4y=0

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

(h, k) = (0, 2), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 2), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 2), b = 2, a = 2

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

4 x^{2} + 25 y^{2} + 4 x - 120 y + 45 = 0

4 x^{2} + y^{2} = 72

64 x^{2} + 25 y^{2} - 16 x - 16 y - 648 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

What is y^2+x^2-4y=0 ?
The solution to y^2+x^2-4y=0 is Ellipse with (h,k)=(0,2),a=2,b=2