Find the eccentricity of the graph of ((x-2)^2/121) + ((y+6)^2/64) = 1 and of 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.

Question

Find the eccentricity of the graph of ((x-2)^2/121) + ((y+6)^2/64) = 1  and of 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.

anonymous · Answer

((x-2)^2/121) + ((y+6)^2/64) = 1

It's a horizontal ellipse as the denominator of x is larger (121 vs 64)

Length of horizontal = a, where a^2 = 121 = eccentrciity

((x-2)^2/121) - ((y+6)^2/64) = 1

Distance between vertices = a, where a^2 = 64