What is x^2-y^2-4x-6y-14=0 ?

The solution to x^2-y^2-4x-6y-14=0 is Hyperbola with (h,k)=(2,-3),a=3,b=3

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x^2-y^2-4x-6y-14=0

x^{2} - y^{2} - 4 x - 6 y - 14 = 0

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

Solution steps

x^{2} - y^{2} - 4 x - 6 y - 14 = 0

Rewrite

x^{2} - y^{2} - 4 x - 6 y - 14 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

(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

What is x^2-y^2-4x-6y-14=0 ?
The solution to x^2-y^2-4x-6y-14=0 is Hyperbola with (h,k)=(2,-3),a=3,b=3