Exploring the foci of an ellipse

The  exercise appears under the Algebra II Math Mission. This exercise practices analyzing information about an ellipse.

Types of Problems
There is one type of problem in this exercise:


 * 1) Use the manipulative and find the values: This problem provides a coordinate plane and an ellipse with movable foci. The student is expected to use the manipulative to find the right position for the ellipse, then use the position to find the values of the constants for the ellipse in standard form.Etfoae1.png

Strategies
Knowledge of all the conics are encouraged to ensure success on this exercise.
 * 1) The center of the ellipse can be found by observing the horizontal and vertical shift of the conic.
 * 2) The radii are the square roots of the numbers under the x^2 and y^2. The major is the larger and the minor is the smaller.
 * 3) If a is the major radius and b is the minor, then c^2=a^2-b^2, where c represents the semi-focal distance (that is, the distance from center to a focus).

Real-life Applications

 * 1) Conics have uses in optics, for making mirrors to reflect light, and acoustics, to amplify sounds.
 * 2) Conics model motion of celestial bodies due to laws of physics.