What is x^2-y^2+1>0 ?

The solution to x^2-y^2+1>0 is Hyperbola with (h,k)=(0,0),a=1,b=1

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x^2-y^2+1>0

x^{2} - y^{2} + 1 > 0

(h, k) = (0, 0), a = 1, b = 1

Solution steps

x^{2} - y^{2} + 1 > 0

Rewrite

x^{2} - y^{2} + 1 > 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{1 ^{2}} - \frac{( x - 0 ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 1, b = 1

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

8 x^{2} - 4 y^{2} - 16 x - 24 = 0

\frac{( y - 1 ) ^{2}}{4} - \frac{( x + 8 ) ^{2}}{25} = 1

3 x^{2} - 4 y^{2} + 3 x + 16 y - 18 = 0

\frac{( x - 5 ) ^{2}}{8 ^{2}} - \frac{( y - 2 ) ^{2}}{6 ^{2}} = 1

What is x^2-y^2+1>0 ?
The solution to x^2-y^2+1>0 is Hyperbola with (h,k)=(0,0),a=1,b=1