What is the center x^2+y^2-10y=0 ?

The center x^2+y^2-10y=0 is (0,5)

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center x^2+y^2-10y=0

center

(0, 5)

Solution steps

x^{2} + y^{2} - 10 y = 0

Rewrite

x^{2} + y^{2} - 10 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 5 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 5), a = 5, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 5), b = 5, a = 5

And the center is:

(0, 5)