An ellipse is inscribed in its auxiliary circle and a point within the circle is chosen at random. If p is the probability that this point lies outside the ellipse and inside the auxiliary circle. Then 8p is equal to (where eccentricity of the ellipse is `sqrt3/2`)
(A) 3 (B) 4 (C) 6 (D) 1

An eppipse of eccentricity (2sqrt2)/(3) is inscribed in a circle and a point within the circle is chosen at random. The probability that this point lies outside the ellipse is

An ellipse is inscribed in a circle and a point within the circle is chosen at random.If the probability that this point lies outside the ellipse is (2)/(3) then the eccentricity of the ellipse is: (A)(2sqrt(2))/(3) (B) (sqrt(5))/(3) (C) (8)/(9)(D)(2)/(3)

A circle of maximum area is inscribed in 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

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. A point is selected at random inside a circle. The probability that the point is closer to the center of the circle than to its circumference is

A square is inscribed in a circle.If p_(r) is the probability that a randomly chosen point inside the circle lies within the square and p, is the probability that the point lies outside the square,then

A square is incribed in a circle . If p_(1) is the probability that a randomly chosen point of the circle lies within the square and p_(2) is the probability that the point lies outside the square then