Elliptical Problem
Geometry
Level
pending
Find the eccentricity of the conic formed by the locus of the in center of the triangle formed by the points P, F, and F' where F and F' the foci of an ellipse and P any random point on it in terms of e where e is the eccentricity of the given ellipse.
√(2e/1+e)
√(e/2(1+e))
e/2
√2e/1+e
√(e/2)
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1 solution
Take point P as acos x and bsin x then apply the formulae to find the in centre of triangle. Then eliminate x and BINGO u get your result