What is 3x^2+3y^2+36y=0 ?

The solution to 3x^2+3y^2+36y=0 is Ellipse with (h,k)=(0,-6),a=6,b=6

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3x^2+3y^2+36y=0

3 x^{2} + 3 y^{2} + 36 y = 0

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

Solution steps

3 x^{2} + 3 y^{2} + 36 y = 0

Rewrite

3 x^{2} + 3 y^{2} + 36 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

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 7 ) ^{2}}{81} = 1

\frac{( x + 1 ) ^{2}}{100} + \frac{( y - 6 ) ^{2}}{64} = 1

\frac{( x - 5 ) ^{2}}{8} + \frac{( y + 1 ) ^{2}}{12} = 1

\frac{x ^{2}}{49} + \frac{y ^{2}}{48} = 1

3 x^{2} + 3 y^{2} + 24 y = 0

What is 3x^2+3y^2+36y=0 ?
The solution to 3x^2+3y^2+36y=0 is Ellipse with (h,k)=(0,-6),a=6,b=6