# Vertex

## The Hyperbola

## Definition

Hyperbola can be defined as the locus of point that moves such that the difference of its distances from two fixed points called the foci is constant. The constant difference is the length of the transverse axis, 2a.

## General Equation

From the general equation of any conic (A and C have opposite sign, and can be A > C, A = C, or A < C.)

$Ax^2 - Cy^2 + Dx + Ey + F = 0 \,$ or

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## Elements of Ellipse

Elements of the ellipse are shown in the figure below.

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## The Ellipse

**Definition of Ellipse**

Ellipse is the locus of point that moves such that the sum of its distances from two fixed points called the foci is constant. The constant sum is the length of the major axis, 2*a*.

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## The Pyramid

A pyramid is a polyhedron with a polygon base of any shape, and all other faces are triangles which have common vertex.

**Properties of a Pyramid**

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## The Prism

Prism is a polyhedron in which two faces are equal polygons in parallel planes, and all other faces are parallelograms. There are two types of prism; oblique prism and right prism. Oblique prism is when the axis is *not* perpendicular to the base and right prism if the axis is parallel to the base. In right prism, all lateral areas are rectangle.

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## Properties of Triangle

**Side**

Side of a triangle is a line segment that connects two vertices. Triangle has three sides, it is denoted by *a*, *b*, and *c* in the figure below.

**Vertex**

Vertex is the point of intersection of two sides of triangle. The three vertices of the triangle are denoted by *A*, *B*, and *C* in the figure below. Notice that the opposite of vertex *A* is side *a*, opposite to vertex *B* is side *B*, and opposite to vertex *C* is side *c*.

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