a)
To find: graph of given parametric equations for different values of
The graph of given parametric equations for different values of
Given information:
Given parametric equations:
Calculation:
Graph of the parametric equations for
By joining the points
Graph of the parametric equations for
By joining the points
Graph of the parametric equations for
By joining the points
Graph of the parametric equations for
By joining the points
Plot all circles as shown in Figure (1).
Figure (1)
b)
To find: rectangular equation after eliminating
After eliminating
Given information:
Given parametric equations:
Formula used:
Calculation:
Elimination of
Compute
Thus, after eliminating
c)
To find: graph of given parametric equations for different values of
The graphs of given parametric equation for different values of
Given information:
The parametric equations:
Also given that
2 | ||||
3 | 3 |
Calculation:
Substitute the values 2 for
The following table shows that the different points of
By joining the points
Figure (2)
Substitute the values
in the parametric equations:
The following table shows that the different points of
By joining the points
Figure (3)
Substitute the values
in the parametric equations:
The following table shows that the different points of
By joining the points
Figure (4)
Substitute the values
in the parametric equations:
The following table shows that the different points of
By joining the points
Figure (5)
d)
To find: rectangular equation after eliminating
After eliminating
Given information:
Given parametric equations:
Formula used:
Calculation:
Elimination of
Compute
Thus, after eliminating
e)
To find: the parametric equation of the circle with center
The parametric equation of the circle with center
Given information:
Center of the circle is
Formula used:
Parametric equation of the circle with center
Calculation:
Substitute
And
Thus, parametric equation of the circle having center
Chapter 6 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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