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

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}

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))