What is -4y^2+9x^2-27x-16y=2 ?

The solution to -4y^2+9x^2-27x-16y=2 is Hyperbola with (h,k)=(3/2 ,-2),a= 5/6 ,b= 5/4

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-4y^2+9x^2-27x-16y=2

- 4 y^{2} + 9 x^{2} - 27 x - 16 y = 2

(h, k) = (\frac{3}{2}, - 2), a = \frac{5}{6}, b = \frac{5}{4}

Solution steps

- 4 y^{2} + 9 x^{2} - 27 x - 16 y = 2

Rewrite

- 4 y^{2} + 9 x^{2} - 27 x - 16 y = 2

in the form of a standard hyperbola equation

\frac{( x - \frac{3}{2} ) ^{2}}{( \frac{5}{6} ) ^{2}} - \frac{( y - ( - 2 ) ) ^{2}}{( \frac{5}{4} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{3}{2}, - 2), a = \frac{5}{6}, b = \frac{5}{4}

x^{2} - 9 y^{2} = 144

- \frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1

19 x^{2} - 6 x - 22 y = 20 y^{2} + 7

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

9 x^{2} - 9 y^{2} = 81

What is -4y^2+9x^2-27x-16y=2 ?
The solution to -4y^2+9x^2-27x-16y=2 is Hyperbola with (h,k)=(3/2 ,-2),a= 5/6 ,b= 5/4