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A curve, called a witch of Maria Agnesi, consists…

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Problem 42 Easy Difficulty

If $ a $ and $ b $ are fixed numbers, find parametric equations for the curve that consists of all possible positions of the point $ P $ in the figure, using the angle $ \theta $ as the parameter. The line segment $ AB $ is tangent to the larger circle.


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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Related Topics

Parametric Equations

Polar Coordinates

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Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

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Samuel Hannah

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Lectures

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16:57

Graphing

In mathematics, a graph is a representation of a set of objects where some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called "vertices" or "nodes", and the relations between them are represented by mathematical abstractions called "edges" or "arcs". The basic notion of a graph was developed by the 17th-century French mathematician Pierre de Fermat, and the term "graph" was coined by the 19th-century mathematician James Joseph Sylvester. The more general mathematical concept of a graph "in which any kind of relation between elements of the set is expressed as an edge, is called a network" (Kolmogorov, "1956, p. 111"). In other words, an undirected graph is a graph in which the edges have no direction associated with them. The most familiar examples of graphs are the graphs of equations. In general, the vertices of a graph can represent concepts and the edges can represent real-valued functions on the concepts, so one can speak of the graph as a function's graph or of the edge as a function's edge.

Video Thumbnail

01:59

Polar Coordinates - Intro

Polar coordinates are a two-dimensional coordinate system that specifies a point in terms of distance from a reference direction (the pole) and angle from a reference direction (the polar axis).

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Problem 16
Problem 17
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Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
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Problem 52

Video Transcript

The problem is, if a and B are fixed, the members find the parametric equations for the curve that consists of our impossible propositions of the pointy in the figure using the angle beta separator life segment it B is tangent to the larger circle. So you think you know it is a coordinate off? He is x y. Then we're half axe is equal to which is equal to Oh, aye, um, steak and data, which is equal to a hams. Second data now why is he called, which is equal to all? See hams sign there, which is equal to eat House sign data. So the parametric equations for the curve. Our accidental toe ate ham sik in the data. Why's he could beat hams, Sign data.

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Calculus: Early Transcendentals

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Related Topics

Parametric Equations

Polar Coordinates

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 2 / BC Courses

Lectures

Video Thumbnail

16:57

Graphing

In mathematics, a graph is a representation of a set of objects where some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called "vertices" or "nodes", and the relations between them are represented by mathematical abstractions called "edges" or "arcs". The basic notion of a graph was developed by the 17th-century French mathematician Pierre de Fermat, and the term "graph" was coined by the 19th-century mathematician James Joseph Sylvester. The more general mathematical concept of a graph "in which any kind of relation between elements of the set is expressed as an edge, is called a network" (Kolmogorov, "1956, p. 111"). In other words, an undirected graph is a graph in which the edges have no direction associated with them. The most familiar examples of graphs are the graphs of equations. In general, the vertices of a graph can represent concepts and the edges can represent real-valued functions on the concepts, so one can speak of the graph as a function's graph or of the edge as a function's edge.

Video Thumbnail

01:59

Polar Coordinates - Intro

Polar coordinates are a two-dimensional coordinate system that specifies a point in terms of distance from a reference direction (the pole) and angle from a reference direction (the polar axis).

Join Course
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