What is 16y^2-9x^2+54x+64y-161=0 ?

The solution to 16y^2-9x^2+54x+64y-161=0 is Hyperbola with (h,k)=(3,-2),a=3,b=4

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16y^2-9x^2+54x+64y-161=0

16 y^{2} - 9 x^{2} + 54 x + 64 y - 161 = 0

(h, k) = (3, - 2), a = 3, b = 4

Solution steps

16 y^{2} - 9 x^{2} + 54 x + 64 y - 161 = 0

Rewrite

16 y^{2} - 9 x^{2} + 54 x + 64 y - 161 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 2), a = 3, b = 4

9 x^{2} - 4 y^{2} - 36 > 0

16 x^{2} - 9 y^{2} - 256 y + 180 x - 452 = 0

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

11 x^{2} - 25 y^{2} + 22 x + 250 y - 889 = 0

x^{2} + 2 x - 100 y^{2} - 1000 y + 2401 = 0

What is 16y^2-9x^2+54x+64y-161=0 ?
The solution to 16y^2-9x^2+54x+64y-161=0 is Hyperbola with (h,k)=(3,-2),a=3,b=4