# 8. 4 hyperbolas homework

What do paths of comets, supersonic booms, ancient Grecian pillars, and natural draft cooling towers have in common? They can all be modeled by the same type of conic. For instance, when something moves faster than the speed of sound, a shock wave in the form of a cone is created. Most people are familiar with the sonic boom created by supersonic aircraft, but humans were breaking the sound barrier long before the first supersonic flight. The crack of a whip occurs because the tip is exceeding the speed of sound. The bullets shot from many firearms also break the sound barrier, although the bang of the gun usually supersedes the sound of the sonic boom.

## Graphing Hyperbolas

## Hyperbolas - Intermediate Algebra 2e | OpenStax

A hyperbola is a conic section that is formed when a plane intersects a double cone, so that it forms two identical curves that go in opposite directions. It has two separate foci and the two branches are mirror images of each other. The two branches of the hyperbola have a transverse axis that bisects them along a line of symmetry and a conjugate axis that is perpendicular to them. The branches mirror each other exactly. Suppose that one branch of the hyperbola has a vertex at 0, 4. The other branch of the hyperbola will have a vertex at 0, Another feature of both branches of the hyperbola is that the sides of each branch come very close to extended diagonal lines, but never quite touch them.

### Lesson Hyperbola (concept and graphing calc.)

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A hyperbola 23 is the set of points in a plane whose distances from two fixed points, called foci, has an absolute difference that is equal to a positive constant. In addition, a hyperbola is formed by the intersection of a cone with an oblique plane that intersects the base. It consists of two separate curves, called branches

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