What is 8x^2+12y^2=96 ?

The solution to 8x^2+12y^2=96 is Ellipse with (h,k)=(0,0),a=2sqrt(3),b=2sqrt(2)

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8x^2+12y^2=96

8 x^{2} + 12 y^{2} = 96

(h, k) = (0, 0), a = 23, b = 22

Solution steps

8 x^{2} + 12 y^{2} = 96

Rewrite

8 x^{2} + 12 y^{2} = 96

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 23, b = 22

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 23, b = 22

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = \frac{x}{6} + \frac{y}{3}

\frac{( x + 1 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{9} = 1

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

\frac{( x - 1.29 ) ^{2}}{1.17} + \frac{y ^{2}}{2.77} = 2

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

What is 8x^2+12y^2=96 ?
The solution to 8x^2+12y^2=96 is Ellipse with (h,k)=(0,0),a=2sqrt(3),b=2sqrt(2)