What is 3x^2+3y^2+24y=0 ?

The solution to 3x^2+3y^2+24y=0 is Ellipse with (h,k)=(0,-4),a=4,b=4

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

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

(h, k) = (0, - 4), a = 4, b = 4

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 4), a = 4, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 4), b = 4, a = 4

5 x^{2} + 7 y^{2} = 9

3 x^{2} + 4 y^{2} - 6 x - 9 = 0

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 7 ) ^{2}}{64} = 1

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

9 x^{2} + 4 y^{2} - 36 x = 0

What is 3x^2+3y^2+24y=0 ?
The solution to 3x^2+3y^2+24y=0 is Ellipse with (h,k)=(0,-4),a=4,b=4