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

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