Concept explainers
(a)
The equation for the following graph:
(a)
Answer to Problem 6CR
Solution:
The equation of the line given in graph is
Explanation of Solution
Given information:
The graph
From the above graph, it is seen that the line passes through the points
The general equation of a straight line passing through two points
Here, the points are
Slope of the line is
Then the equation of the line passing through the points
Hence the equation of the line given in graph is
(b)
The equation for the following graph of circle:
(b)
Answer to Problem 6CR
Solution:
The equation of the circle given in the graph is
Explanation of Solution
Given information:
The graph
From the above graph, it is seen that the center of the given circle is
The general equation of the circle having center at
Here,
Then, the equation of the given circle by substituting the above values is
Hence, the equation of the circle given in graph is
(c)
The equation for the following graph of ellipse:
(c)
Answer to Problem 6CR
Solution:
The equation of the ellipse given in the graph is
Explanation of Solution
Given information:
The graph
From the above graph, it is seen that the center of the given ellipse is
The general equation of the ellipse having center at
Here,
Then, the equation of the given ellipse by substituting the above values is
Hence, the equation of the ellipse given in the graph is
(d)
The equation for the following graph of parabola:
(d)
Answer to Problem 6CR
Solution:
The equation of the parabola given in graph is
Explanation of Solution
Given information:
The graph
From the above graph, it is seen that the center of the given parabola is
The general equation of the parabola which opens up having center at
Here,
Then, the equation of the given parabola by substituting the above values is
As the parabola passes through the point
Substitute this point
Now, to get the equation of the parabola, substitute the value of
Hence, the equation of the parabola given in the graph is
(e)
The equation for the following graph of hyperbola:
(e)
Answer to Problem 6CR
Solution:
The equation of the hyperbola given in the graph is
Explanation of Solution
Given information:
The graph
From the above graph, it is seen that the center of the given hyperbola is
The general equation of the hyperbola whose transverse axis is along the
Here,
Then, the equation of the given hyperbola by substituting the above values is
As the hyperbola passes through the point
Substitute this point
Now, to get the equation of the parabola, substitute the value of
Hence, the equation of the hyperbola given in the graph is
(f)
The equation for the following graph of exponential function:
(f)
Answer to Problem 6CR
Solution:
The equation of the exponential function given in graph is
Explanation of Solution
Given information:
The graph
From the above graph, it is seen that the exponential function has
and passes through the point
The general equation of the exponential function is
Plug the
Then, the equation of the exponential function becomes
The equation of the given exponential function passes through the point
Substitute this point
Now, to get the equation of the exponential function, substitute the value of
Hence, the equation of the exponential function given in the graph is
Chapter 10 Solutions
Precalculus Enhanced with Graphing Utilities
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