Find the equation of the ellipse whose eccentricity is `1/2`, one of the foci is (2, 3) and a directrix is x = 7. Also find the length of the major and minor axes of the ellipse.

Find the equation of the ellipse if centres is (3,-4) one of the foci is (3+sqrt(3), -4) and e= sqrt(3)/2

Find the equation of an ellipse whose eccentricity is 2/3, the latus rectum is 5 and the centre is at the origin.

Find the equation of the ellipse whose length of minor axis is 16 and foci are (0, +- 6) .

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) .

Find the equation of the ellipse whose vertices are (+-13,0) and foci are (+-5,0)

Find the equation of the ellipse, whose length of the major axis is 20 and foci are (0,+-5)

Find the equation of parabola whose focus is (0,1) and the directrix is x+2=0. Also find the vertex of the parabola.

For the ellipse x^(2)+ 3y^(2) = a^(2) find the length of major and minor axis.

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)