What is the eccentricity x^2-y^2<1 ?

The eccentricity x^2-y^2<1 is square root of 2

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eccentricity x^2-y^2<1

eccentricity

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

2

Solution steps

= \frac{a ^{2} + b ^{2}}{a}

Rewrite as

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

Calculate Hyperbola properties

x^{2} - y^{2} = 1 :

Right-left Hyperbola with

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

= \frac{1 ^{2} + 1 ^{2}}{1}

Refine

= 2

\frac{x ^{2}}{4} - \frac{( y + 1 ) ^{2}}{16} = 1

x^{2} - 4 y^{2} - 2 x + 16 y = 20

5 y^{2} - 16 x^{2} + 400 = 0

\frac{y ^{2}}{9} - \frac{x ^{2}}{16} = 1

\frac{x ^{2}}{25} - \frac{y ^{2}}{36} = 1

What is the eccentricity x^2-y^2<1 ?
The eccentricity x^2-y^2<1 is square root of 2