   Chapter 10.1, Problem 93E

Chapter
Section
Textbook Problem

# True or False? In Exercises 91–96, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If C is the circumference of the ellipse. x 2 a 2 + y 2 b 2 = 1 ,         b < a then   2 π b ≤ C ≤ 2 π a .

To determine

Whether the statement, “If C is the circumference of the ellipse, x2a2+y2b2=1,b<a then 2πbC2πa” is true or false.

Explanation

Consider the parabola, x2a2+y2b2=1,b<a.

Now, all the ellipses are circle if their eccentricity is 1. This means that an ellipse will change into a circle if a=b.

Now, it is given in the statement that b<a. So, the ellipse has an abscissa as its major axis and ordinate as its minor axis.

Thus, the ellipse, x2a2+y2b2=1,b<a could have a maximum circumference of a circle of radius a and a minimum circumference of a circle of radius b

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