What is 2x^2-3x-2y^2+6y=1 ?

The solution to 2x^2-3x-2y^2+6y=1 is Hyperbola with (h,k)=(3/4 , 3/2),a=(sqrt(19))/4 ,b=(sqrt(19))/4

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2x^2-3x-2y^2+6y=1

2 x^{2} - 3 x - 2 y^{2} + 6 y = 1

(h, k) = (\frac{3}{4}, \frac{3}{2}), a = \frac{19}{4}, b = \frac{19}{4}

Solution steps

2 x^{2} - 3 x - 2 y^{2} + 6 y = 1

Rewrite

2 x^{2} - 3 x - 2 y^{2} + 6 y = 1

in the form of a standard hyperbola equation

\frac{( y - \frac{3}{2} ) ^{2}}{( \frac{19}{4} ) ^{2}} - \frac{( x - \frac{3}{4} ) ^{2}}{( \frac{19}{4} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{3}{4}, \frac{3}{2}), a = \frac{19}{4}, b = \frac{19}{4}

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

y^{2} - z^{2} = 1

\frac{( y - h ) ^{2}}{49} - \frac{( x - k ) ^{2}}{81} = 1

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

(x - 5)^{2} - (y - 2)^{2} = 1

What is 2x^2-3x-2y^2+6y=1 ?
The solution to 2x^2-3x-2y^2+6y=1 is Hyperbola with (h,k)=(3/4 , 3/2),a=(sqrt(19))/4 ,b=(sqrt(19))/4