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}

x^{2} = \frac{x}{2} + y^{2}

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{1} = 1

\frac{( x - 0 ) ^{2}}{3 ^{2}} - \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

x^{2} - 4 y^{2} + 2 x + 16 y - 11 = 0

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

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)