Question

A circle of maximum area is inscribed inside an ellipse. If p is the probability that a point within the ellipse chosen at random lies outside the circle, then the eccentricity of the ellipse is

A.√(1-p) B. √{1-(1-p)²} C. √(1-p²) D.√{(1+p)²-1}

Answer 1

Let length of minor axis=2a
lenght of major axis=2b
Then area of circle=πa^2
area of ellipse=πab
ie, p=(πab-πa^2)/πab
=1-a/b
Therefore a/b=1-p
So eccentricity of ellipse=√(1-(a/b)^2)
=√(1-(1-p)^2)