What is 9x^2-16y^2-54x-64y-127=0 ?

The solution to 9x^2-16y^2-54x-64y-127=0 is Hyperbola with (h,k)=(3,-2),a=4,b=3

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

4 x^{2} - 5 y^{2} = 7

\frac{1}{x ^{2} - y ^{2}} \geq 1

- x^{2} + 2 y^{2} + 6 x - 7 y = 7

16 y^{2} - 9 x^{2} + 90 x - 64 y - 305 = 0

\frac{x ^{2}}{12} - \frac{y ^{2}}{4} = 1

What is 9x^2-16y^2-54x-64y-127=0 ?
The solution to 9x^2-16y^2-54x-64y-127=0 is Hyperbola with (h,k)=(3,-2),a=4,b=3