What is x^2-y^2-6x+16y-119=0 ?

The solution to x^2-y^2-6x+16y-119=0 is Hyperbola with (h,k)=(3,8),a=8,b=8

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x^2-y^2-6x+16y-119=0

x^{2} - y^{2} - 6 x + 16 y - 119 = 0

(h, k) = (3, 8), a = 8, b = 8

Solution steps

x^{2} - y^{2} - 6 x + 16 y - 119 = 0

Rewrite

x^{2} - y^{2} - 6 x + 16 y - 119 = 0

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{8 ^{2}} - \frac{( y - 8 ) ^{2}}{8 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 8), a = 8, b = 8

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

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

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

y^{2} - 4 x^{2} < 1

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

What is x^2-y^2-6x+16y-119=0 ?
The solution to x^2-y^2-6x+16y-119=0 is Hyperbola with (h,k)=(3,8),a=8,b=8