What is 16x^2-y^2-32x-6y-57=0 ?

The solution to 16x^2-y^2-32x-6y-57=0 is Hyperbola with (h,k)=(1,-3),a=2,b=8

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16x^2-y^2-32x-6y-57=0

16 x^{2} - y^{2} - 32 x - 6 y - 57 = 0

(h, k) = (1, - 3), a = 2, b = 8

Solution steps

16 x^{2} - y^{2} - 32 x - 6 y - 57 = 0

Rewrite

16 x^{2} - y^{2} - 32 x - 6 y - 57 = 0

in the form of a standard hyperbola equation

\frac{( x - 1 ) ^{2}}{2 ^{2}} - \frac{( y - ( - 3 ) ) ^{2}}{8 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, - 3), a = 2, b = 8

\frac{y ^{2}}{25} - \frac{( x + 1 ) ^{2}}{16} = 1

6 x^{2} - 5 y^{2} + 36 x + 20 y - 16 = 0

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

y^{2} - 8 x^{2} - 2 x - y = 0

\frac{x ^{2}}{64} - \frac{y ^{2}}{16} = 1

What is 16x^2-y^2-32x-6y-57=0 ?
The solution to 16x^2-y^2-32x-6y-57=0 is Hyperbola with (h,k)=(1,-3),a=2,b=8