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Find the (i) lengths of major axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity, and (v) length of the latus rectum of each of the following ellipses.

16x^{2} + 25y^{2} = 400

x^{2} + 4y^{2} = 100

9x^{2} + 16y^{2} = 144

4x^{2} + 9y^{2} = 1

3x^{2} + 2y^{2} = 18

9x^{2} + y^{2} = 36

16x^{2} + y^{2} = 16

25x^{2} + 4y^{2} = 100

Find the equation of the ellipse whose vertices are at (±6, 0) and foci at (±4, 0).

Find the equation of the ellipse whose vertices are the (0, ±4) and foci at .

Find the equation of the ellipse the ends of whose major and minor axes are (±4, 0) and (0, ±3) respectively.

The length of the major axis of an ellipse is 20 units, and its foci are . Find the equation of the ellipse.

Find the equation of the ellipse whose foci are (±2, 0) and the eccentricity is .

Find the equation of the ellipse whose foci are at (±1, 0) and .

Find the equation of the ellipse whose foci are at (0, ±4) and .

Find the equation of the ellipse with center at the origin, the major axis on the x-axis and passing through the points (4, 3) and (-1, 4).

Find the equation of the ellipse with eccentricity , foci on the y-axis, center at the origin and passing through the point (6, 4).

Find the equation of the ellipse which passes through the point (4, 1) and having its foci at (±3, 0).

Find the equation of an ellipse, the lengths of whose major and mirror axes are 10 and 8 units respectively.

Find the equation of an ellipse whose eccentricity is , the latus rectum is 5, and the center is at the origin.

Find the eccentricity of an ellipse whose latus rectum is one half of its minor axis.

Find the eccentricity of an ellipse whose latus rectum is one half of its major axis.