Posts Tagged ‘focus’

Directrix of a Parabola

Thursday, October 15th, 2009

How to Find the Directrix of a Parabola

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Description

A detailed tutorial on how to find the directrix of a parabola. Step by step tutorial including several examples of how to find the directrix of a parabola for reference.

Overview

A parabola is a curved shape that is formed by the graph of the function x squared. A parabola is technically known as the locus of points where the distance to the focus equals the distance to the directrix. The directrix is a given line on a parabola that does not go through the focus.

Linear Regression

Friday, October 9th, 2009

Introduction to Linear Regression

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Description

A detailed tutorial on linear regression. Step by step tutorial including several example problems of linear regression for reference.

Overview

Regression is a type of analysis that is used for analyzing several variables when the focus is on a dependent variable and one or more independent variables. Linear regression is when the dependent variable is a linear combination of the parameters. It can be used for both straight lines and parabolas, and each has a different formula.

Straight Line: y_i=\beta_0 +\beta_1 x_i +\varepsilon_i,\quad i=1,\dots,N.\!

Parabola: y_i=\beta_0 +\beta_1 x_i +\beta_2 x_i^2+\varepsilon_i,\ i=1,\dots,N.\!

Hyperbola

Tuesday, September 29th, 2009

Definition of a Hyperbola

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Description

A detailed tutorial of the definition of a hyperbola. Step by steo tutorial including several examples of the definition of a hyperbola for reference.

Overview

A hyperbola is similar to a parabola, but there is one difference – the hyperbola has two branches. You can think of it in the 2D form as a concave up parabola on top of a concave down parabola. Many people refer to the hyperbola as the “bow” because that is what it resembles. Like the parabola, a hyperbola is caused by the intersection of a conical surface and a plane.

Parabola

Tuesday, September 29th, 2009

Definition of a Parabola

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Description

 

A detailed tutorial of the definition of a parabola. Step by step tutorial including a visual example of the definition of a parabola for reference.

 

Overview

 

A parabola is an elongated curve that is used often in graphing. A parabola is formed by the graph of y = x^2, and its traditional form is concave up. Technically, the parabola is actually a conic section, which is the intersection of a conical surface and a plane parallel to the generated straight line of that surface.

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