Concept explainers
a.
Describe the effect on the graph when
a.
Answer to Problem 83E
The curve become wider.
Explanation of Solution
Given information:
Consider the parabola
Use a graphing utility to graph the parabola for
Calculation:
Consider the equation of parabola,
Now Use a graphing utility to graph the parabola for
Hence, the curve become wider as increases the value of
b.
Locate the focus for each parabola.
b.
Answer to Problem 83E
Explanation of Solution
Given information:
Consider the parabola
Locate the focus for each parabola in part (a).
Calculation:
Consider the equation of parabola,
Now Use a graphing utility to graph the parabola for
We need to locate the focus for each parabola drawn above, Since each parabola has its axis vertical, the focus is located at the point
Hence the foci are located at
c.
How can the length of the latus rectum be determined directly from the standard form of the equation of the parabola?
c.
Answer to Problem 83E
Explanation of Solution
Given information:
Consider the parabola
For each parabola in part (a), find the length of the latus rectum (see figure). How can the length of the latus rectum be determined directly from the standard form of the equation of the parabola?
Calculation:
Find the length of the latus rectum for each parabola drawn in part
Let consider the case of the parabola with
The equation of parabola is,
Also, the focus as found above is
Thus the point at which the latus rectum intersects the parabola has its
Now substitute
Thus, the length of the latus rectum is
Since the length of the latus rectum in other cases be
Hence, the length of the latus rectum is
d.
Explain how the result of part (c) can be used.
d.
Answer to Problem 83E
locate two points in the parabola quite easily
Explanation of Solution
Given information:
Consider the parabola
Explain how the result of part (c) can be used as a sketching aid when graphing parabolas.
Calculation:
The latus rectum can be useful since it gives us two points on the parabola directly by looking at its standard equation.
Since we can locate two points in the parabola quite easily.
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning