`Pa n dQ` are the foci of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and `B` is an end of the minor axis. If `P B Q` is an equilateral triangle, then the eccentricity of the ellipse is `1/(sqrt(2))` (b) `1/3` (d) `1/2` (d) `(sqrt(3))/2`

S and T are the foci of the ellipse x^2/a^2+y^2/b^2 = 1 and B is an end of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is e then find value of 4e

If S\ a n d\ S ' are two foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1\ a n d\ B is and end of the minor axis such that triangle B S S ' is equilateral, then write the eccentricity of the ellipse.

S and T are foci of an ellipse and B is an end of the minor axis , if STB is an equilateral triangle , the eccentricity of the ellipse , is

S and T are foci of an ellipse and B is an end of the minor axis , if STB is an equilateral triangle , the eccentricity of the ellipse , is

A parabola is drawn with focus at one of the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If the latus rectum of the ellipse and that of the parabola are same, then the eccentricity of the ellipse is (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these

There are exactly two points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 whose distances from its center are the same and are equal to (sqrt(a^2+2b^2))/2dot Then the eccentricity of the ellipse is 1/2 (b) 1/(sqrt(2)) (c) 1/3 (d) 1/(3sqrt(2))

If the ellipse x^2/a^2+y^2/b^2=1 (b > a) and the parabola y^2 = 4ax cut at right angles, then eccentricity of the ellipse is (a) (3)/(5) (b) (2)/(3) (c) (1)/(sqrt(2)) (d) (1)/(2)

P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with AA ' as the major axis. Find the maximum area of triangle A P A '

Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.

Let Sa n dS ' be two foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If a circle described on S S^(prime) as diameter intersects the ellipse at real and distinct points, then the eccentricity e of the ellipse satisfies (a) e=1/(sqrt(2)) (b) e in (1/(sqrt(2)),1) (c) e in (0,1/(sqrt(2))) (d) none of these