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

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

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2x^2+3y^2=4

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

(h, k) = (0, 0), a = 2, 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 - 1 ) ^{2}}{49} + \frac{( y - 3 ) ^{2}}{36} = 1

(2 x - 9)^{2} + (y)^{2} = 5^{2}

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

25 x^{2} + 4 y^{2} - 100 = 0

x^{2} + 4 y^{2} = 46

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