The eccentricity of an ellipse is `(2)/(3)` focus is S(5,4) and the major axis and directrix intersect at Z(8,7) . Find the coordinates of the centre of the ellipse .

The eccentricity of an ellipse is (1)/(2) , focus is S (0,0) and the major axis and directrix intersect at Z (-1,-1) . Find the coordinates of the centre of the ellipse .

The eccentricity of an ellipse is (1)/(sqrt(3)) , the coordinates of focus is (-2,1) and the point of intersection of the major axis and the directrix is (-2,3) . Find the coordinates of the centre of the ellipse and also equation of the ellipse .

The eccentricity of an ellipse is (1)/(2) and its one focus is at S(3,2) , if the vertex nearer of S be A (5,4) , find the equation of the ellipse .

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 eccentricity of an ellipse is (2)/(3) and the coordinates of its focus and the corresponding vertex are (1,2) and (2,2) respectively. Find the equation of the ellipse . Also find the coordinate of the point of intersection of its major axis and the directrix in the same direction .

Find the latus rectum , eccentricity and the coordinates of the foci of the ellipse 9x^(2) + 5y^(2) + 30 y = 0

Find the eccentricity of the ellipse if the length of rectum is equal to half the minor axis of the ellipse .

The coordinates of the focus of an ellipse are (1,2) and eccentricity is (1)/(2) , the equation of its directrix is 3x + 4y - 5 = 0 . Find the equation of the ellipse.

Find the equation of an ellipse with eccentricity 1/2 , focus F(1,1) and the line x-y+3 =0 as directrix.

One the x-y plane, the eccentricity of an ellipse is fixed (in size and position) by 1) both foci 2) both directrices 3)one focus and the corresponding directrix 4)the length of major axis.