a.
To find: Whether the graph of the equation is a parabola, an ellipse or a hyperbola.
a.
Answer to Problem 57RE
The graph of the equation is an ellipse
Explanation of Solution
Given information:
The equation of the graph is
Concept used:
The general equation of the form
The discremanant is
If
If
Calculation:
The given equation is
Comparing with general equation
Conclusion:
Since
The equation represents an ellipse.
b.
To eliminate:
b.
Answer to Problem 57RE
Required equation after eliminating
Explanation of Solution
Given information:
The equation of the graph is
Concept used:
Let
Using this find
The new axis will be
Substitute x & y in the given equation t obtain the required equation.
Calculation:
Comparing the given equation
with the general equation
Substitute the values find
The new axis are
Substitute a and y in given equation
Simplifying the above equation
Conclusion:
Therefore the required equation after eliminating the
c.
To sketch: The graph of the given equation
c.
Answer to Problem 57RE
From the graph it can be observed that the given equation represents an ellipse.
Explanation of Solution
Given information:
Given equation of graph is
Graph:
The graph is obtained as:
Interpretation:
From the above graph it can be observed that the given equation represents an ellipse.
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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