What is 3x^2+3y^2+12y=0 ?

The solution to 3x^2+3y^2+12y=0 is Ellipse with (h,k)=(0,-2),a=2,b=2

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3x^2+3y^2+12y=0

3 x^{2} + 3 y^{2} + 12 y = 0

(h, k) = (0, - 2), a = 2, b = 2

Solution steps

3 x^{2} + 3 y^{2} + 12 y = 0

Rewrite

3 x^{2} + 3 y^{2} + 12 y = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, - 2), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 2), b = 2, a = 2

\frac{( x + 1 ) ^{2}}{22.33} + \frac{( y - 1 ) ^{2}}{16.75} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{11} = 1

4 x^{2} + 2 y^{2} - 7 x + y - 5 = 0

225 x^{2} + 289 y^{2} = 65.025

\frac{x ^{2}}{4} + \frac{3 x}{2} + 9 y^{2} - 18 y + 9 = 0

What is 3x^2+3y^2+12y=0 ?
The solution to 3x^2+3y^2+12y=0 is Ellipse with (h,k)=(0,-2),a=2,b=2