What is 2x^2-3y^2=1 ?

The solution to 2x^2-3y^2=1 is Hyperbola with (h,k)=(0,0),a=sqrt(1/2),b=sqrt(1/3)

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2x^2-3y^2=1

2 x^{2} - 3 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{3}

Solution steps

2 x^{2} - 3 y^{2} = 1

Rewrite

2 x^{2} - 3 y^{2} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{1}{3}

9 x^{2} - 4 y^{2} + 36 x - 16 y - 16 = 0

y^{2} = - 0.8944 + 1.125 x^{2}

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

(5 x - 4)^{2} = (8 y + 2) \cdot y

4 x^{2} - 8 y^{2} \leq 12

What is 2x^2-3y^2=1 ?
The solution to 2x^2-3y^2=1 is Hyperbola with (h,k)=(0,0),a=sqrt(1/2),b=sqrt(1/3)