Question

Find the eccentricity of the graph of (x-2)^2/121+(y+6)^2/64=1 and the graph of (x-2)^2/121-(y+6)^2/64=1. Using complete sentences compare the eccentricity of the graph of an ellipse with the graph of a hyperbola.

Answer 1

The angle between the line of eccentricity and the axis will always be less than 45° for an ellipse but greater than 45° for a hyperbola.
As the eccentricity approaches zero the ellipse becomes more circular, only when the eccentricity unity is the curve of a parabola, when the eccentricity rises over unity the curve becomes a hyperbola and the higher the eccentricity the straighter the curve becomes.