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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

3 x^{2} - 2 y^{2} + 6 x - 8 y - 17 = 0

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

4 x^{2} - 3 y^{2} = 11

a^{2} - b^{2} = 2018 - 2 a

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

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