What is (x^2)/4+x/2-(y^2)/9-(2y)/9+1/6 =0 ?

The solution to (x^2)/4+x/2-(y^2)/9-(2y)/9+1/6 =0 is Hyperbola with (h,k)=(-1,-1),a= 1/2 ,b= 1/3

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(x^2)/4+x/2-(y^2)/9-(2y)/9+1/6 =0

\frac{x ^{2}}{4} + \frac{x}{2} - \frac{y ^{2}}{9} - \frac{2 y}{9} + \frac{1}{6} = 0

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

Solution steps

\frac{x ^{2}}{4} + \frac{x}{2} - \frac{y ^{2}}{9} - \frac{2 y}{9} + \frac{1}{6} = 0

Rewrite

\frac{x ^{2}}{4} + \frac{x}{2} - \frac{y ^{2}}{9} - \frac{2 y}{9} + \frac{1}{6} = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

\frac{y ^{2}}{56} - \frac{x ^{2}}{56} = 1

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{4} = 1

4 (y - 4)^{2} - (x - 2)^{2} = 36

\frac{( x - 3 ) ^{2}}{16 + ( y + 5 ) ^{2}} = 1

What is (x^2)/4+x/2-(y^2)/9-(2y)/9+1/6 =0 ?
The solution to (x^2)/4+x/2-(y^2)/9-(2y)/9+1/6 =0 is Hyperbola with (h,k)=(-1,-1),a= 1/2 ,b= 1/3