What is the asymptotes of x^2-y^2<1 ?

The asymptotes of x^2-y^2<1 is y=x,\quad y=-x

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asymptotes of x^2-y^2<1

asymptotes

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

y = x, y = - x

Solution steps

y = \pm \frac{b}{a} (x - h) + k

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

y = \frac{1}{1} (x - 0) + 0, y = - \frac{1}{1} (x - 0) + 0

Refine

y = x, y = - x

\frac{( x + 5 ) ^{2}}{4} - \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{25} - \frac{y ^{2}}{16} = 1

2 x^{2} - 2 y^{2} - 20 x + 16 y + 16 = 0

25 y^{2} - 16 x^{2} - 400 = 0

9 (y - 2)^{2} - 4 x^{2} = 36

What is the asymptotes of x^2-y^2<1 ?
The asymptotes of x^2-y^2<1 is y=x,\quad y=-x