Table of Contents

# Conic Section

A conic section is a curve in mathematics that is defined by the intersection of a plane and a cone. There are four types of conic sections: ellipses, parabolas, hyperbolas, and circles. Each type is defined by specific properties of the curve.

## Conic Section Definition

A conic section is the curve formed by the intersection of a plane and a cone. There are four types of conic sections: the ellipse, the parabola, the hyperbola, and the circle.

## Conic Equation

A conic equation is an equation that describes a conic section. A conic section is a geometric shape that is formed when a plane intersects a cone. There are four basic types of conic equations: the parabola, the ellipse, the hyperbola, and the circle.

## Graphing Conic Sections

There are four types of conic sections: circles, ellipses, parabolas, and hyperbolas.

- To graph a conic section, you need to know the equation of the conic section.
- The equation of a circle is x^2 + y^2 = r^2.
- The equation of an ellipse is x^2/a^2 + y^2/b^2 = 1.
- The equation of a parabola is y = x^2.
- The equation of a hyperbola is xy = c.

## Circle of Fifths

The Circle of Fifths is a diagram that illustrates how the major keys are related to one another. The diagram is a circle with each key represented by a different color. The colors progress around the circle in a clockwise direction, starting with C major.

The Circle of Fifths is helpful for understanding how chords are related to one another. For example, if you want to create a chord progression in the key of C major, you can use chords that are found in the C major section of the Circle of Fifths.

## Parabola

The parabola is a curve in mathematics that is shaped like an upside-down U. It is used in physics to model the path of a projectile.

## Ellipse

An ellipse is a closed curve that is formed by the intersection of a plane and a cone.

## Hyperbola

The hyperbola is a conic section with two branches, each of which is a hyperbola.

The hyperbola is a curve that can be formed by the intersection of a plane with a cone. If the plane is parallel to the base of the cone, the curve will be a circle. If the plane is not parallel to the base of the cone, the curve will be a hyperbola.

There are two branches of a hyperbola, each of which is a hyperbola in its own right. The branches intersect each other at two points, called the vertices of the hyperbola. The distance between the two branches is called the hyperbola’s focal length.

The hyperbola has the equation:

\begin{align}

x^2 – y^2 = a^2

\end{align}

where a is the focal length.

## Facts to Remember

1. The Electoral College is a process, not a place.

2. The Electoral College is made up of 538 electors.

3. A presidential candidate needs to win 270 electoral votes to win the election.

4. The Electoral College is not a representative body.

5. The votes of the electors are not cast until December 19th.

6. The president is not elected by the popular vote.

7. The president is elected by the Electoral College.