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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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Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

Missouri State University

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

16:57

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.

01:59

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).

03:25

If a and $b$ are fixed num…

02:12

If $a$ and $b$ are fixed n…

01:25

01:42

01:56

If $ a $ and $ b $ are fix…

03:45

02:59

02:22

Finding Parametric Equatio…

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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