What is 4x^{(2)}+y^{(2)}=2y ?

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

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

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

(h, k) = (0, 1), a = \frac{1}{2}, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 1), a = \frac{1}{2}, 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 = \frac{1}{2}

\frac{x ^{2}}{49} + \frac{y ^{2}}{40} = 1

3 = \frac{x ^{2}}{4} + \frac{y ^{2}}{9}

\frac{( x - 3 ) ^{2}}{49} + \frac{( y - 5 ) ^{2}}{16} = 1

\frac{x ^{2}}{64} + \frac{( y - 3 ) ^{2}}{9} = 1

4 x^{2} + z^{2} = 16

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