What is 64x^2+128x-9y^2-72y-656=0 ?

The solution to 64x^2+128x-9y^2-72y-656=0 is Hyperbola with (h,k)=(-1,-4),a=3,b=8

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64x^2+128x-9y^2-72y-656=0

64 x^{2} + 128 x - 9 y^{2} - 72 y - 656 = 0

(h, k) = (- 1, - 4), a = 3, b = 8

Solution steps

64 x^{2} + 128 x - 9 y^{2} - 72 y - 656 = 0

Rewrite

64 x^{2} + 128 x - 9 y^{2} - 72 y - 656 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 1 ) ) ^{2}}{3 ^{2}} - \frac{( y - ( - 4 ) ) ^{2}}{8 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, - 4), a = 3, b = 8

x^{2} - 3 y^{2} - 2 x = 0

\frac{( x + 5 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

6 x^{2} - 9 y^{2} + 96 x + 36 y + 252 = 0

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

\frac{( y + 4 ) ^{2}}{16} - \frac{( x - 3 ) ^{2}}{25} = 1

What is 64x^2+128x-9y^2-72y-656=0 ?
The solution to 64x^2+128x-9y^2-72y-656=0 is Hyperbola with (h,k)=(-1,-4),a=3,b=8