branches of curve of hyperbola: There are two branches of curve of hyperbola **X² / a² – Y² / b ² =1** we see this equation of hyperbola as** | x| → ∞, | y | → ∞** so we can extend branches to **infinity** and more detail by hyperbola equation.branches of curve of hyperbola image:

x ² / a ² – y ² / b ² = 1 …………………………. A

The curve is symmetric with respect to both the axis. We can write equation A

y ² / b ² = x ² / a ² – 1

y ² = b ² / a ² (x ² – a ²)

y = ± b / a √ x ² – a ² …………………… B

**branches of curve of hyperbola:**

** (1) Branch of curve |x| < a**

If **|x| < a,** then y is **imaginary** so that no portion of the curve lies between

-a < x < a For x ≥ a ,

so that the point on the curve lies below the corresponding point on the line** y = b / a (x)**

in the **first quadrant**

And in this case the points on the curve lies

above the line in the **fourth quadrant.**

**Branches of curve of hyperbola**

**(2)Branch of curve |x| < – a**

If x ≤ -a then, by similar arguments,

lies below the corresponding point

on in **second quadrant.**

If then the curve lie above the corresponding point on in

third quadrant

Standard hyperbola table

Equation | ||

Foci | (± c, 0) | (0, ± c) |

Direct rices | ||

trance verse axis | y = 0 | x =0 |

Vertices | (± a , 0) | (0, ± a) |

Eccentricity | e = c / a > 1 | e = c / a >1 |

center | (0, 0) | (0, 0) |

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