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

The solution to 4x^2+y^2=4y is Ellipse with (h,k)=(0,2),a=1,b=2

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4x^2+y^2=4y

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

(h, k) = (0, 2), a = 1, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 2), a = 1, 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 = 1

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

- x^{2} - \frac{y ^{2}}{49} = 1

\frac{( x + 7 ) ^{2}}{144} + \frac{( y + 2 ) ^{2}}{100} = 1

\frac{x ^{2}}{36} + \frac{( y + 9 ) ^{2}}{81} = 1

4 x^{2} + 18 y^{2} = 36

What is 4x^2+y^2=4y ?
The solution to 4x^2+y^2=4y is Ellipse with (h,k)=(0,2),a=1,b=2