What is 16x^2-9y^2+96x-72y+144=0 ?

The solution to 16x^2-9y^2+96x-72y+144=0 is Hyperbola with (h,k)=(-3,-4),a=4,b=3

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16x^2-9y^2+96x-72y+144=0

16 x^{2} - 9 y^{2} + 96 x - 72 y + 144 = 0

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

Solution steps

16 x^{2} - 9 y^{2} + 96 x - 72 y + 144 = 0

Rewrite

16 x^{2} - 9 y^{2} + 96 x - 72 y + 144 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{81} - \frac{y ^{2}}{61} = 1

\frac{( x - 27 ) ^{2}}{3} - \frac{( y - 4 ) ^{2}}{5} = 1

2 x^{2} - 3 y^{2} = 47

- 9 x^{2} + 4 y^{2} = 144

\frac{( x + 3 ) ^{2}}{9} - \frac{( y - 4 ) ^{2}}{16} = 1

What is 16x^2-9y^2+96x-72y+144=0 ?
The solution to 16x^2-9y^2+96x-72y+144=0 is Hyperbola with (h,k)=(-3,-4),a=4,b=3