Let the distance between a focus and the corresponding directrix of an ellipse be 8 and the eccentricity be `1/2` . If the length of the minor axis is `k ,` then `(sqrt(3)k)/2` is ____________

Find the equation of ellipse having focus at (1,2) corresponding directirx x-y+2=0 and eccentricity 0.5 .

Find the equation of the ellipse whose one of the foci is (2,0) and the corresponding directrix is x = 8 and eccentricity is (1)/(2) .

If the length of latus rectum is 5/2 and eccentricity is 1/2 , then the equation of the ellipse is

The euqaiton of the conic with focus (2,-1) directrix x - y = 0 and eccentricity 1/2 is

Find the equation of the ellipse whose focus is S(+-1, -1), the corresponding directrix is x -y+3=0, and eccentricity is 1/2. Also find its center, the second focus, the equation of the second directrix, and the length of latus rectum.

The length of the major axis of an ellipse is three times the length of minor axis, its eccentricity is . . . .

The angle between the lines joining the foci of an ellipse to an extremity of its minor axis is 90^@ . The eccentricity is

The length of the latus rectum of an ellipse in 1/3 of its major axis. Its eccentricity is :

If the focal distance of the one end of the minor axis of standard ellipse is k and distance between its foci is 2h(kgth) , then find its equation.

Consider two straight lines, each of which is tangent to both the circle x^2+y^2=1/2 and the parabola y^2=4x . Let these lines intersect at the point Q . Consider the ellipse whose center is at the origin O(0,\ 0) and whose semi-major axis is O Q . If the length of the minor axis of this ellipse is sqrt(2) , then which of the following statement(s) is (are) TRUE? For the ellipse, the eccentricity is 1/(sqrt(2)) and the length of the latus rectum is 1 (b) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2 (c) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(4sqrt(2))(pi-2) (d) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(16)(pi-2)