To find:theexplanation that the central rectangle of a hyperbola can be used to sketch its asymptotes.
Explanation of Solution
Given information:
The given statement is “the central rectangle of a hyperbola can be used to sketch its asymptotes”.
Calculation:
Let’s take following figure of a hyperbola with transverse axis horizontal.
The equation of the hyperbola is given by.
The central rectangle of the hyperbola is constructed with dimensions
Then the asymptotes are the lines given by
It is easily verified that the corners of the central rectangle lie on the asymptotes.
That is
Similarly, the central rectangle and asymptotes for a hyperbola with transverse axis vertical can be constructed.
Therefore, the central rectangle of a hyperbola can be used to sketch its asymptotes is proved.
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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