To find: The center, vertices, foci, asymptotes and graph of hyperbola
Answer to Problem 28E
The center of the hyperbola is
Explanation of Solution
Given information:
Given equation of hyperbola is
Calculation:
Compare the given equation with the standard equation of hyperbola
The center of the hyperbola is given as
The vertices of the hyperbola is given by
So the vertices are
The foci of the hyperbola is given by
Hence the foci are
The asymptotes of the hyperbola is given by
Substitute
To draw the graph of hyperbola, solve the equations of hyperbola in terms of
Simplify further to find the value of y.
Use the above equation and the asymptotes to draw the graph of the hyperbola.
Figure (1)
Therefore The center of the hyperbola is
Verify the result using graphical utility:
Draw the graph for the hyperbola using the graphical utility.
From the above, it is clear that both the graphs are similar.
Hence, proved.
Chapter 9 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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