What is -3y^2+18x^2=-y-2 ?

The solution to -3y^2+18x^2=-y-2 is Hyperbola with (h,k)=(0, 1/6),a= 5/6 ,b= 5/(6sqrt(6))

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-3y^2+18x^2=-y-2

- 3 y^{2} + 18 x^{2} = - y - 2

(h, k) = (0, \frac{1}{6}), a = \frac{5}{6}, b = \frac{5}{6 6}

Solution steps

- 3 y^{2} + 18 x^{2} = - y - 2

Rewrite

- 3 y^{2} + 18 x^{2} = - y - 2

in the form of a standard hyperbola equation

\frac{( y - \frac{1}{6} ) ^{2}}{( \frac{5}{6} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{5}{6 6} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, \frac{1}{6}), a = \frac{5}{6}, b = \frac{5}{6 6}

9 a^{2} - b^{2} + 81 = 13 a - 18 b - 81

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

x^{2} = 2 y^{2} + 6

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

36 y^{2} - 5 x^{2} = 180

What is -3y^2+18x^2=-y-2 ?
The solution to -3y^2+18x^2=-y-2 is Hyperbola with (h,k)=(0, 1/6),a= 5/6 ,b= 5/(6sqrt(6))