What is x^2+y^2-8y=0 ?

The solution to x^2+y^2-8y=0 is Ellipse with (h,k)=(0,4),a=4,b=4

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x^2+y^2-8y=0

x^{2} + y^{2} - 8 y = 0

(h, k) = (0, 4), a = 4, b = 4

Solution steps

x^{2} + y^{2} - 8 y = 0

Rewrite

x^{2} + y^{2} - 8 y = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 4), a = 4, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 4), b = 4, a = 4

9 x^{2} + 16 y^{2} - 18 x - 64 y - 71 = 0

(x - a)^{2} + (y - b)^{2} = 1

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

16 (x - 1)^{2} + 4 (y - 4)^{2} = 64

9 x^{2} + 5 y^{2} + 18 x - 10 y - 31 = 0

What is x^2+y^2-8y=0 ?
The solution to x^2+y^2-8y=0 is Ellipse with (h,k)=(0,4),a=4,b=4