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

The center x^2+4*y^2-4*y=0 is (0, 1/2)

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

center

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

(0, \frac{1}{2})

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

And the center is:

(0, \frac{1}{2})

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