What is 9x^2+12y^2=108 ?

The solution to 9x^2+12y^2=108 is Ellipse with (h,k)=(0,0),a=2sqrt(3),b=3

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9x^2+12y^2=108

9 x^{2} + 12 y^{2} = 108

(h, k) = (0, 0), a = 23, b = 3

Solution steps

9 x^{2} + 12 y^{2} = 108

Rewrite

9 x^{2} + 12 y^{2} = 108

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 23, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 23, b = 3

x^{2} + 3 y^{2} + 4 x + 18 y + 22 = 0

36 x^{2} - 36 x + 64 y^{2} + 256 y + 265 = 576

x^{2} + y^{2} - 14 y = 0

\frac{x ^{2}}{( 2.67 ) ^{2}} + \frac{y ^{2}}{( 2.85 ) ^{2}} = 1

\frac{x ^{2}}{45} + \frac{y ^{2}}{9} = 1

What is 9x^2+12y^2=108 ?
The solution to 9x^2+12y^2=108 is Ellipse with (h,k)=(0,0),a=2sqrt(3),b=3