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

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

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x^2+y^2+6y<0

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

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

Solution steps

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

Rewrite

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

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

4 x^{2} + 9 y^{2} + 12 x - 18 y - \frac{83}{4} = 0

9 x^{2} + 25 y^{2} - 18 x - 100 y - 3 = 0

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

14 x^{2} + 11 y^{2} - 252 x - 22 y + 991 = 0

\frac{( x + 4 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{25} = 1

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