10. Parametric Equations

Graphing Parametric Equations

Textbook Question
In Exercises 21–40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that −∞ < t < ∞.x = 2ᵗ, y = 2⁻ᵗ; t ≥ 0
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Textbook Question
In Exercises 53–56, find two different sets of parametric equations for each rectangular equation.y = 4x − 3
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Textbook Question
In Exercises 53–56, find two different sets of parametric equations for each rectangular equation.y = x² + 4
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Textbook Question
In Exercises 57–58, the parametric equations of four plane curves are given. Graph each plane curve and determine how they differ from each other.x = t and y = t² − 4
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Textbook Question
In Exercises 59–62, sketch the plane curve represented by the given parametric equations. Then use interval notation to give each relation's domain and range.x = t² + t + 1, y = 2t
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Textbook Question
In Exercises 71–76, eliminate the parameter and graph the plane curve represented by the parametric equations. Use arrows to show the orientation of each plane curve.x = 2t − 1, y = 1 − t; −∞ < t < ∞
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Textbook Question
In Exercises 71–76, eliminate the parameter and graph the plane curve represented by the parametric equations. Use arrows to show the orientation of each plane curve.x = 3 + 2 cos t, y = 1+2 sin t; 0 ≤ t < 2π
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Textbook Question
Find two different sets of parametric equations for y = x² + 6.
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Textbook Question
For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. See Examples 1 and 2.

x = t + 2 , y = t ―4 , for t in (― ∞ , ∞)
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Textbook Question
Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.

x = 2 cos t , y = 2 sin t
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Textbook Question
Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.

x = 4 sin t , y = 3 cos t
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Textbook Question
Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.

x = 2 + sin t , y = 1 + cos t
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Textbook Question
Graph each plane curve defined by the parametric equations for t in [0, 2π] Then find a rectangular equation for the plane curve. See Example 3.

x = 1 + cos t , y = sin t ― 1
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