What is 9x^2+6y^2+36y=0 ?

The solution to 9x^2+6y^2+36y=0 is Ellipse with (h,k)=(0,-3),a=sqrt(6),b=3

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9x^2+6y^2+36y=0

9 x^{2} + 6 y^{2} + 36 y = 0

(h, k) = (0, - 3), a = 6, b = 3

Solution steps

9 x^{2} + 6 y^{2} + 36 y = 0

Rewrite

9 x^{2} + 6 y^{2} + 36 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 6 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 3), a = 6, 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 = 6

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

3 x^{2} + 2 y^{2} = 4

16 x^{2} + 4 y^{2} = 64

8 x^{2} + 2 y^{2} + 16 x = 0

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

What is 9x^2+6y^2+36y=0 ?
The solution to 9x^2+6y^2+36y=0 is Ellipse with (h,k)=(0,-3),a=sqrt(6),b=3