In Problems 7 − 26 , graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve. x ( t ) = t 2 + 4 , y ( t ) = t 2 − 4 ; − ∞ < t < ∞
In Problems 7 − 26 , graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve. x ( t ) = t 2 + 4 , y ( t ) = t 2 − 4 ; − ∞ < t < ∞
Solution Summary: The author explains how to draw the parametric equation by plugging some values of t in the given equation and finding few points on the curve.
In Problems
7
−
26
,
graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve.
x
(
t
)
=
t
2
+
4
,
y
(
t
)
=
t
2
−
4
;
−
∞
<
t
<
∞
Two objects E and F are traveling by the following parametrically defined functions
x = 2t - 4 x = 2ty = t - 1 y = t + 1
a. If the paths of the objects E and F intersect at (6,4), at what time do they intersect if the parameter t stands for time?
b. Write an equation d(t) that represents the distance between the two objects E and F at any point in time. Graph d(t).
c. What do you notice about the graph of d(t)? What does this tell us about the objects E and F?
1. Let A = (1, -2, 2), B = (0, -1, 3), and C = (2,c-4, c), where c is a real-valued constant.
Find all values of c for which the magnitude of AB x AC is 3√2.
(a)
(b)
ABC.
For c = 3, find the parametric equations of the line passing through C and perpendicular to the triangle
5. Graph and find the parametric equations for the line through the point (1, -2, 3) and parallel to
the line r
(1 – 2t, 3t, -5 + t).
Chapter 9 Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY