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

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

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

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

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

Solution steps

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

Rewrite

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

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{x ^{2}}{16} + \frac{( y + 1 ) ^{2}}{4} - 1 = 0

\frac{( x ^{2} )}{25} + \frac{( y ^{2} )}{9} = 1

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

\frac{x ^{2}}{16} + \frac{y ^{2}}{12} = 1

y^{2} - x - 4 y + 3 = 0

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