What is the axis 2x^2+3y^2=4 ?

The axis 2x^2+3y^2=4 is semi-major axis a=sqrt(2), semi-minor axis b= 2/(sqrt(3))

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axis 2x^2+3y^2=4

axis

2 x^{2} + 3 y^{2} = 4

semi - major axis a = 2, semi - minor axis b = \frac{2}{3}

Solution steps

2 x^{2} + 3 y^{2} = 4

Rewrite

2 x^{2} + 3 y^{2} = 4

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 4 ) ^{2}}{64} + \frac{( y - 2 ) ^{2}}{39} = 1

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

10 x^{2} + 4 y^{2} + 2 x + 16 y = 144

\frac{( x + 8 ) ^{2}}{64} + \frac{( y - 11 ) ^{2}}{36} = 1

5 x^{2} + 20 y^{2} = 50

What is the axis 2x^2+3y^2=4 ?
The axis 2x^2+3y^2=4 is semi-major axis a=sqrt(2), semi-minor axis b= 2/(sqrt(3))