What is 0=x^2+y^2+6y ?

The solution to 0=x^2+y^2+6y is Ellipse with (h,k)=(0,-3),a=3,b=3

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0=x^2+y^2+6y

0 = x^{2} + y^{2} + 6 y

(h, k) = (0, - 3), a = 3, b = 3

Solution steps

0 = x^{2} + y^{2} + 6 y

Rewrite

0 = x^{2} + y^{2} + 6 y

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 3), a = 3, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 3), b = 3, a = 3

\frac{X ^{2}}{25} + \frac{Y ^{2}}{9} = 1

\frac{x ^{2}}{20} + \frac{y ^{2}}{36} = 1

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

4 (x - 3)^{2} + (y - 2)^{2} = 4

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

What is 0=x^2+y^2+6y ?
The solution to 0=x^2+y^2+6y is Ellipse with (h,k)=(0,-3),a=3,b=3