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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{144} = 1

25 x^{2} - 16 y^{2} + 250 x + 32 y + 109 = 0

16 y^{2} - x^{2} + 2 x + 64 y + 47 = 0

x^{2} + 2 x - y^{2} + 6 y = 15

5 x^{2} - 4 y^{2} - 20 x + 24 y - 36 = 0

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