# focus

## The Parabola

### Definition of Parabola

Parabola is the locus of point that moves such that it is always equidistant from a fixed point and a fixed line. The fixed point is called focus and the fixed line is called directrix.

### General Equations of Parabola

From the general equation of all conic sections, either $A$ or $C$ is zero to form a parabolic section.

For $A = 0$, the equation will reduce to $Cy^2 + Dx + Ey + F = 0$ or

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## 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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## Conic Sections

**Definition**

Conic sections can be defined as the locus of point that moves so that the ratio of its distance from a fixed point called the focus to its distance from a fixed line called the directrix is constant. The constant ratio is called the eccentricity of the conic.

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