# Conics - Hyperbola

##### Intros

###### Lessons

- Hyperbola:

horizontal hyperbola vertical hyperbola

• Graph looks sort of like two mirrored parabolas, with the two "halves" being called "branches".

• "Vertices" are defined similarly to the way of a "vertex" is defined for a parabola.

• Just as the focus for a parabola, the two foci for a hyperbola are inside each branch.

• The line connecting the two vertices is called the "transverse axis".

##### Examples

###### Lessons

**properties of a hyperbola**

$-(\frac{x-6}{4})^2 + (\frac{y+5}{3})^2=1$

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###### Topic Notes

hyperbola: the

ellipse: the

$c= \sqrt{a^2 - b^2}$ $c$: distance from the center to a focus

$e= \frac{c}{a}$ $e$: eccentricity; the larger the value of $e$, the straighter the hyperbola

**difference**of the distances from any point on a hyperbola to each focus is constant and equal to the transverse axis $2a$.ellipse: the

**sum**of the distances from any point on an ellipse to each focus is constant and equal to the major axis $2a$.$c= \sqrt{a^2 - b^2}$ $c$: distance from the center to a focus

$e= \frac{c}{a}$ $e$: eccentricity; the larger the value of $e$, the straighter the hyperbola

###### Basic Concepts

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