How can i identify in the graph of an ellipse where is b, a, c, the vertices, the foci, the latus rectum, the essentricity and the directrix.

Please reply. Needed for my studies tonight :/ midterm exam tom. :/

http://www.youtube.com/watch?v=8A1BsHbXWBE

latus rectum:
http://www.emathzone.com/tutorials/geometry/length-of-latus-rectum-of-ellipse.html

To identify the features of an ellipse on a graph, you need to understand the standard form of an ellipse equation and the definitions of its various components. Let's go step by step to identify each element:

1. Identifying 'a' and 'b': The standard form of the equation of an ellipse centered at the origin is (x^2/a^2) + (y^2/b^2) = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis. By comparing the lengths of the major and minor axes in the graph, you can determine the values of 'a' and 'b'.

2. Identifying 'c' (distance from the center to the foci): The distance 'c' is related to 'a' and 'b' using the equation c^2 = a^2 - b^2. You can calculate 'c' by taking the square root of the difference between 'a' and 'b' squared.

3. Locating the vertices: The vertices of an ellipse are the points where the ellipse intersects its major axis. The major axis is the longer axis, and its length is twice 'a'. So, from the center, move 'a' units in the positive and negative directions along the x-axis to locate the vertices.

4. Locating the foci: The foci of an ellipse are the points located along the major axis, inside the ellipse, such that the sum of the distances from any point on the ellipse to the two foci is constant. The distance between each focus and the center is 'c'. From the center, move 'c' units in the positive and negative directions along the x-axis to locate the foci.

5. Finding the latus rectum: The latus rectum is the line segment passing through one focus and perpendicular to the major axis, with the length equal to 2b^2/a. You can find the equation of the latus rectum by using the slope of the major axis and the coordinates of one focus.

6. Calculating the eccentricity: The eccentricity of an ellipse is the ratio of the distance between the foci and the length of the major axis. It can be found using the formula e = c/a, where 'e' is the eccentricity.

7. Determining the directrix: The directrix is a line parallel to the minor axis, located outside the ellipse. Its distance from the center is a^2/c. You can find the equation of the directrix by using the slope of the major axis and the coordinates of one focus.

Note: If the ellipse is not centered at the origin (0,0), you would need to translate it first by subtracting the x-coordinate of the center from 'x' and the y-coordinate of the center from 'y'. Then, apply the above steps.

Remember to review each step carefully and practice identifying these elements on different ellipse graphs. Good luck on your midterm exam!