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

The solution to x^2+y^2-10y=0 is Ellipse with (h,k)=(0,5),a=5,b=5

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

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

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

16 x^{2} + 25 y^{2} - 64 x + 150 y - 111 = 0

25 x^{2} + 9 y^{2} - 225 = 0

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

x^{2} + 4 y^{2} - 6 x + 5 = 0

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{9} = 1

What is x^2+y^2-10y=0 ?
The solution to x^2+y^2-10y=0 is Ellipse with (h,k)=(0,5),a=5,b=5