What is 64x^2-36y^2+192x+36y-441=0 ?

The solution to 64x^2-36y^2+192x+36y-441=0 is Hyperbola with (h,k)=(-3/2 , 1/2),a=3,b=4

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64x^2-36y^2+192x+36y-441=0

64 x^{2} - 36 y^{2} + 192 x + 36 y - 441 = 0

(h, k) = (- \frac{3}{2}, \frac{1}{2}), a = 3, b = 4

Solution steps

64 x^{2} - 36 y^{2} + 192 x + 36 y - 441 = 0

Rewrite

64 x^{2} - 36 y^{2} + 192 x + 36 y - 441 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- \frac{3}{2}, \frac{1}{2}), a = 3, b = 4

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

\frac{( x + 5 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{36} = 2

\frac{x ^{2}}{9} - \frac{y ^{2}}{27} = 1

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

\frac{( y + 4 ) ^{2}}{64} - \frac{( x + 3 ) ^{2}}{25} = 1

What is 64x^2-36y^2+192x+36y-441=0 ?
The solution to 64x^2-36y^2+192x+36y-441=0 is Hyperbola with (h,k)=(-3/2 , 1/2),a=3,b=4