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

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

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

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

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

Solution steps

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

Rewrite

x^{2} + y^{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

x^{2} = - 8 y

f (x) = (x - 3)^{2}

x^{2} + 9 y^{2} + 6 x - 90 y + 225 = 0

x^{2} = - 4 y

x^{2} + y^{2} + 10 x + 12 y + 25 = 0

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