What is x^2+y^2+12y^2-108=0 ?

The solution to x^2+y^2+12y^2-108=0 is Ellipse with (h,k)=(0,0),a=6sqrt(3),b=(6sqrt(3))/(sqrt(13))

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x^2+y^2+12y^2-108=0

x^{2} + y^{2} + 12 y^{2} - 108 = 0

(h, k) = (0, 0), a = 63, b = \frac{6 3}{13}

Solution steps

x^{2} + y^{2} + 12 y^{2} - 108 = 0

Rewrite

x^{2} + y^{2} + 12 y^{2} - 108 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 6 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{6 3}{13} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 63, b = \frac{6 3}{13}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 63, b = \frac{6 3}{13}

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

x^{2} + 4 y^{2} - 6 x - 32 y + 72 = 0

(- y^{2}) = x^{2} + 12

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

\frac{x ^{2}}{580 0 ^{2}} + \frac{y ^{2}}{150 0 ^{2}} = 1

What is x^2+y^2+12y^2-108=0 ?
The solution to x^2+y^2+12y^2-108=0 is Ellipse with (h,k)=(0,0),a=6sqrt(3),b=(6sqrt(3))/(sqrt(13))