21, The notion of eccentricity for ellipses is the same for hyperbolas in that we can define the eccentricity e for a hyperbola as distance from the center to a focus e = distance from the center to a vertex a. Explain why e>1 for any hyperbola. b. Find the equation of the hyperbola with vertices (+3,0) and eccentricity e=2.
21, The notion of eccentricity for ellipses is the same for hyperbolas in that we can define the eccentricity e for a hyperbola as distance from the center to a focus e = distance from the center to a vertex a. Explain why e>1 for any hyperbola. b. Find the equation of the hyperbola with vertices (+3,0) and eccentricity e=2.
Chapter11: Conics
Section11.4: Hyperbolas
Problem 184E: In your own words, define a hyperbola and write the equation of a hyperbola centered at the origin...
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Transcribed Image Text:21, The notion of eccentricity for ellipses is the same for hyperbolas in that we can define the
eccentricity e for a hyperbola as
distance from the center to a focus
e =
distance from the center to a vertex
a. Explain why e>1 for any hyperbola.
b. Find the equation of the hyperbola with vertices (+3,0) and eccentricity e=2.
C. Find the eccentricity of each of the hyperbolas in Exercises 1-4.
d. Describe how the shape of the hyperbola changes as the eccentricity increases.
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