Students will learn what the foci of a hyperbola are, in terms of distance between each focus and the hyperbola. Then students will learn how to derive the focal length formula for an ellipse.
Concude by giving your students this challenge:
Cycling Squares by NRICH: The trick is to find numbers which can be paired with only one or two of the remaining numbers. Such pairs, or triples, must occur in the loop. Notice, for example, that 2 can only be paired with 14, to make 16, or 34, to make 36. Thus, the sequence 14, 2, 36, or its reverse, must occur in the loop. Next, you would remove 2 from your list of available numbers, because it's surrounded, namely, by 14 and 34. Then you'd continue in this way until no numbers remain. Reading the loop clockwise, starting at 2, the solution is: 2, 34, 30, 19, 17, 8, 28, 21, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14.