What is 9x^2-16y^2+54x-32y-79=0 ?

The solution to 9x^2-16y^2+54x-32y-79=0 is Hyperbola with (h,k)=(-3,-1),a=4,b=3

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9x^2-16y^2+54x-32y-79=0

9 x^{2} - 16 y^{2} + 54 x - 32 y - 79 = 0

(h, k) = (- 3, - 1), a = 4, b = 3

Solution steps

9 x^{2} - 16 y^{2} + 54 x - 32 y - 79 = 0

Rewrite

9 x^{2} - 16 y^{2} + 54 x - 32 y - 79 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, - 1), a = 4, b = 3

x, x = 3.4 h (x)^{2} - 8 h - 4 x^{2} + 8 x

x^{2} - 3 y^{2} - 3 x = y + 5

x^{2} - 92 y^{2} = 1

6 x^{2} - 8 y^{2} + 12 x - 32 y = 178

\frac{4 ( x + 2 ) ^{2}}{25} - \frac{( y + 3 ) ^{2}}{9} = 1

What is 9x^2-16y^2+54x-32y-79=0 ?
The solution to 9x^2-16y^2+54x-32y-79=0 is Hyperbola with (h,k)=(-3,-1),a=4,b=3