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

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

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x^2+y^2=-8y

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

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

Solution steps

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

Rewrite

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

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

3 y^{2} + 5 x^{2} = 20

\frac{( x - 4 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{20} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{8} = 1

4 x^{2} + 9 y^{2} + 24 x = 0

\frac{x ^{2}}{81} + \frac{y ^{2}}{25} = 1

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