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

The solution to 3x^2-2y^2=4 is Hyperbola 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 a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

(x + y) (x - y) = 1

\frac{( y + 2 ) ^{2}}{9} - \frac{( x + 2 ) ^{2}}{4} = 1

18 x^{2} - 9 y^{2} - 96 x - 36 y - 36 = 0

\frac{x ^{2}}{14} - \frac{y ^{2}}{20} = 1

y^{2} - 2 x^{2} - 16 = 0

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