An ellipse has `O B` as the semi-minor axis, `Fa n dF '` as its foci, and `/_F B F '` a right angle. Then, find the eccentricity of the ellipse.

An ellipse has O B as the semi-minor axis, F and F ' as its foci, and /_F B F ' a right angle. Then, find the eccentricity of the ellipse.

An ellipse has OB as a semi-minor axis, F and F' are its two foci and the angle FBF' is a right angle. Find the eccentricity of the ellipse.

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

If the tangent at any point of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosbeta/(cosalpha)

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

The tangent at a point P(acosvarphi,bsinvarphi) of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 meets its auxiliary circle at two points, the chord joining which subtends a right angle at the center. Find the eccentricity of the ellipse.

The latus rectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is

If the angle between the lines joining the end points of minor axis of an elipes with its one focus is pi/2, then the eccentricity of the ellipse is-

The eccentricity of an ellipse is (4)/(5) and the coordinates of its one focus and the corresponding vertex are (8,2) and (9,2) . Find the equation of the ellipse. Also find in the same direction the coordinates of the point of intersection of its major axis and the directrix.

The tangent at the point theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , meets its auxiliary circle at two points whose join subtends a right angle at the centre, show that the eccentricity of the ellipse is given by, (1)/(e^(2))=1+sin^(2)theta