Ellipse and Functions

Geometry Level 3

Consider an ellipse with its major and minor axes along the X and Y axis respectively.The ellipse has its foci at (1,0) and (-1,0) respectively and has its eccentricity as 0.5.

Let line L be a tangent to the ellipse at some point on it.Let point S be the reflection of the focus ( lying on positive X axis) in the line L. Find the locus of S.

Now consider a function f having its domain as the set of real numbers and its range a subset of the set of real numbers,this function f has the property that it is simultaneously even as well as odd function.

Calculate the area bounded between the function f and the locus of point S.It is given that the bounded area contains points whose y coordinate is non negative.

Round off the answer (ie the bounded area) to the nearest integer and submit.


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