What is 9y^2+36y+4x^2=0 ?

The solution to 9y^2+36y+4x^2=0 is Ellipse with (h,k)=(0,-2),a=3,b=2

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9y^2+36y+4x^2=0

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

(h, k) = (0, - 2), a = 3, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, - 2), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, - 2), a = 3, b = 2

16 x^{(2)} + 25 y^{(2)} - 128 x + 100 y = 0

\frac{( x + 2 ) ^{2}}{64} + \frac{( y - 8 ) ^{2}}{36} = 1

16 x^{2} + 25 y^{2} = \frac{169}{4}

\frac{( x - 3 ) ^{2}}{16} + (\frac{( y + 4 )}{9})^{2} = 1

9 x^{2} + 5 y^{2} = 180

What is 9y^2+36y+4x^2=0 ?
The solution to 9y^2+36y+4x^2=0 is Ellipse with (h,k)=(0,-2),a=3,b=2