Problem 12E

How does the eccentricity determine the type of conic section?

Solution 12E

Step 1:

the eccentricity , denoted e or is a parameter associated with every conic section. It can be thought of as a measure of how much the conic section deviates from being circular.

In particular,

The eccentricity of a circle is zero.

The eccentricity of an ellipse which is not a circle is greater than zero but less than 1.

The eccentricity of a parabola is 1.

The eccentricity of a hyperbola is greater than 1.

The eccentricity of a line is infinite.

Furthermore, two conic sections are similar (identically shaped) if and only if they have the same eccentricity.