What is 3x^2+2y^2=8 ?

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

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3x^2+2y^2=8

3 x^{2} + 2 y^{2} = 8

(h, k) = (0, 0), a = \frac{2 2}{3}, b = 2

Solution steps

3 x^{2} + 2 y^{2} = 8

Rewrite

3 x^{2} + 2 y^{2} = 8

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2 2}{3}, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 2, a = \frac{2 2}{3}

\frac{( x + 1 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

\frac{x ^{2}}{256} + \frac{y ^{2}}{400} = 1

\frac{( x - 1 ) ^{2}}{13} + \frac{( y + 5 ) ^{2}}{12} = 1

x^{2} + 2 y^{2} - 8 y - 32 = 0

\frac{x ^{2}}{324} + \frac{y ^{2}}{400} = 1

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