What is 2x^2-3y^2-x+y=0 ?

The solution to 2x^2-3y^2-x+y=0 is Hyperbola with (h,k)=(1/4 , 1/6),a= 1/(4sqrt(3)),b= 1/(6sqrt(2))

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2x^2-3y^2-x+y=0

2 x^{2} - 3 y^{2} - x + y = 0

(h, k) = (\frac{1}{4}, \frac{1}{6}), a = \frac{1}{4 3}, b = \frac{1}{6 2}

Solution steps

2 x^{2} - 3 y^{2} - x + y = 0

Rewrite

2 x^{2} - 3 y^{2} - x + y = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{1}{4} ) ^{2}}{( \frac{1}{4 3} ) ^{2}} - \frac{( y - \frac{1}{6} ) ^{2}}{( \frac{1}{6 2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{4}, \frac{1}{6}), a = \frac{1}{4 3}, b = \frac{1}{6 2}

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

2 a - 3 b^{2} = 4 a^{2} - 9 b^{2}

\frac{( y - 4 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{16} = 1

9 x^{2} - 36 x - y^{2} - 6 y + 18 = 0

x^{2} - y^{2} - y + 9 = 0

What is 2x^2-3y^2-x+y=0 ?
The solution to 2x^2-3y^2-x+y=0 is Hyperbola with (h,k)=(1/4 , 1/6),a= 1/(4sqrt(3)),b= 1/(6sqrt(2))