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Could somebody please explain the method for answering a question like this?

Caleb James Coppersmith
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It is easy to see, that the curve in definition of $A$ is an ellipse. Hence the set of extreme points of $A$ is this ellipse. Convexity is obvious: we use the same arguments as in the case of a closed ball.

Przemysław Scherwentke
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  • @CalebJamesCoppersmith I am not sure, which tools you can use. But again for a unit ball i ${\bf R}^2$ it is easy to see that no point of its sphere is a linear combination of points from the ball (in this case we will have an interval on the sphere. An ellipse is obtained by a linear transformation of a sphere, hence all the arguments are valid. (I assume that arguments, showing, that you understand the problem, are enough. If not, one can take two points and compute, where lies a point from the interior of an inteerval with these ends). – Przemysław Scherwentke Nov 02 '14 at 02:09