What is x^2+y^2+12y=0 ?

The solution to x^2+y^2+12y=0 is Ellipse with (h,k)=(0,-6),a=6,b=6

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x^2+y^2+12y=0

x^{2} + y^{2} + 12 y = 0

(h, k) = (0, - 6), a = 6, b = 6

Solution steps

x^{2} + y^{2} + 12 y = 0

Rewrite

x^{2} + y^{2} + 12 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{6 ^{2}} + \frac{( y - ( - 6 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 6), a = 6, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 6), b = 6, a = 6

9 x^{2} + 25 y^{2} + 108 x - 200 y + 4 = 0

9 x^{2} + 16 y^{2} + 18 x - 32 y - 119 = 0

\frac{x ^{2}}{16} + \frac{( y - 1 ) ^{2}}{36} = 1

\frac{2 x - x ^{2} - y ^{2}}{x ^{2} + y ^{2} - x} \leq 0

x^{2} + 2 - 6 x = - 5 z^{2} + 2

What is x^2+y^2+12y=0 ?
The solution to x^2+y^2+12y=0 is Ellipse with (h,k)=(0,-6),a=6,b=6