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(a) Eliminate the parameter to find a Cartesian equation of the curve.(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as parameter increases.

$ x = e^t $, $ \quad y = e^{-2t} $

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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

Campbell University

Baylor University

Boston College

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).

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(a) Eliminate the paramete…

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eliminate the parameter to…

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Consider the following…

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the problem is part, eh? Eliminates the perimeter to find a Kardashian equation of the curve at a half. Why is he called you too? You It is a powerful negative too, which is equal to ax to the power ofthe native to this is equal to one over x squared. This is a cottage in question. Off the roof had be scarce, the kerf and indicated with an arrow the direction in which the kerf is trist as having two increases. The first notice that axe is greatest and zero so we can schedule the curve as follows. We can see what he is equal to. Zero actually Goto one. Why is he going to one? And when he is, he called to one slacks. You see what he why is he going to be connected to half this direction Is the direction invention the crew for the trist as permitted increases

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