What is 9x^2+36x-8y^2+64y=164 ?

The solution to 9x^2+36x-8y^2+64y=164 is Hyperbola with (h,k)=(-2,4),a=2sqrt(2),b=3

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9x^2+36x-8y^2+64y=164

9 x^{2} + 36 x - 8 y^{2} + 64 y = 164

(h, k) = (- 2, 4), a = 22, b = 3

Solution steps

9 x^{2} + 36 x - 8 y^{2} + 64 y = 164

Rewrite

9 x^{2} + 36 x - 8 y^{2} + 64 y = 164

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 2, 4), a = 22, b = 3

9 x^{2} - 16 y^{2} + 144 x + 32 y + 79 = 0

0 = y^{2} - y - \frac{x ^{2}}{4} + 24

4 x^{2} - 9 y^{2} - 16 x + 36 y + 16 = 0

\frac{x ^{2}}{16} - \frac{y ^{2}}{7} = 1

\frac{x ^{2}}{64} - \frac{y ^{2}}{81} = 1

What is 9x^2+36x-8y^2+64y=164 ?
The solution to 9x^2+36x-8y^2+64y=164 is Hyperbola with (h,k)=(-2,4),a=2sqrt(2),b=3