What is 36x^2-9y^2+216x+36y=-207 ?

The solution to 36x^2-9y^2+216x+36y=-207 is Hyperbola with (h,k)=(-3,2),a= 3/2 ,b=3

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36x^2-9y^2+216x+36y=-207

36 x^{2} - 9 y^{2} + 216 x + 36 y = - 207

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

Solution steps

36 x^{2} - 9 y^{2} + 216 x + 36 y = - 207

Rewrite

36 x^{2} - 9 y^{2} + 216 x + 36 y = - 207

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

- 4 x^{2} + y^{2} + 8 x - 20 = 0

\frac{( y - 7 ) ^{2}}{32} - \frac{( x - 1 ) ^{2}}{64} = 1

36 x^{2} - 16 y^{2} - 144 x + 128 y - 265 = 0

16 x^{2} - y^{2} = 1

9 x^{2} - 16 y^{2} - 54 x - 64 y - 127 = 0

What is 36x^2-9y^2+216x+36y=-207 ?
The solution to 36x^2-9y^2+216x+36y=-207 is Hyperbola with (h,k)=(-3,2),a= 3/2 ,b=3