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

The solution to 3x^2+2y^2=4 is Ellipse with (h,k)=(0,0),a= 2/(sqrt(3)),b=sqrt(2)

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3x^2+2y^2=4

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

16 x^{2} + 4 y^{2} = 64

8 x^{2} + 2 y^{2} + 16 x = 0

4 x^{2} + y^{2} - 4 y = 0

\frac{x ^{2}}{16} + \frac{( y + 1 ) ^{2}}{4} - 1 = 0

\frac{( x ^{2} )}{25} + \frac{( y ^{2} )}{9} = 1

What is 3x^2+2y^2=4 ?
The solution to 3x^2+2y^2=4 is Ellipse with (h,k)=(0,0),a= 2/(sqrt(3)),b=sqrt(2)