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

\frac{( x - 6 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{9} = 1

\frac{x ^{2}}{33} - \frac{y ^{2}}{3} = 1

x^{2} - 4 x - y^{2} - 6 y - 2 = 0

\frac{( y + 3 ) ^{2}}{64} - \frac{( x + 1 ) ^{2}}{36} = 1

- 4 x^{2} + 9 y^{2} + 24 x - 36 y - 32 = 0

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