Science:Math Exam Resources/Courses/MATH101/April 2008/Question 07 (b)/Statement

Let E be the ellipse x² + k²y² = 1, where k is a constant with k ≥ 1. Let S be the region inside the circle x² + y² = 1, outside E, and above the x-axis.

Find all values of k such that the centroid (centre of mass) of S lies inside S (i.e. outside E). You may use the result of part (a).