What is 16x^2-9y^2+32x+72y-704=0 ?

The solution to 16x^2-9y^2+32x+72y-704=0 is Hyperbola with (h,k)=(-1,4),a=6,b=8

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16x^2-9y^2+32x+72y-704=0

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

(h, k) = (- 1, 4), a = 6, b = 8

Solution steps

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

Rewrite

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 1 ) ) ^{2}}{6 ^{2}} - \frac{( y - 4 ) ^{2}}{8 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 4), a = 6, b = 8

16 x^{2} - 25 y^{2} = 400

\frac{y ^{2}}{25} - \frac{x ^{2}}{4} = 1

\frac{x ^{2}}{144} - \frac{y ^{2}}{81} = 1

y^{2} = x^{2} + 1

4 y^{2} - 9 x^{2} = 36

What is 16x^2-9y^2+32x+72y-704=0 ?
The solution to 16x^2-9y^2+32x+72y-704=0 is Hyperbola with (h,k)=(-1,4),a=6,b=8