Observe the shapes of the hyperbolas in Examples 2 and 3. Which hyperbola has the larger eccentricity? Confirm your answer by computing the eccentricity of each hyperbola.
The eccentricity of a hyperbola is defined as e = c > a. For a hyperbola, c > a > 0, so e > 1 when e is close to 1, a hyperbola appears to be very narrow as the eccentricity increases, the hyperbola becomes "wider."