What is 16x^2-9y^2-64x-18y+199=0 ?

The solution to 16x^2-9y^2-64x-18y+199=0 is Hyperbola with (h,k)=(2,-1),a=4,b=3

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16x^2-9y^2-64x-18y+199=0

16 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

(h, k) = (2, - 1), a = 4, b = 3

Solution steps

16 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

Rewrite

16 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, - 1), a = 4, b = 3

4 x^{2} - 8 y^{2} = 3

y^{2} = x^{2} + 9

x^{2} - y^{2} + 2 x - y = 0

y^{2} - 4 y - 4 x^{2} + 8 x - 4 = 0

- 9 x^{2} - 32 y = - 16 y^{2} + 128

What is 16x^2-9y^2-64x-18y+199=0 ?
The solution to 16x^2-9y^2-64x-18y+199=0 is Hyperbola with (h,k)=(2,-1),a=4,b=3