Question 1:

P (x,y ) F (-C,0) G (-a, 0) (a,0) (c, 0 ) Figure 2.3.1-3 C: Hyperbola: Given: Two fixed points F, G and a fixed positive number k. The hyperbola con- sists of all points P such that FP - GP = k. 1. Follow the procedures outlined for the Ellipse noting that the substitution b2 = c2 - a2 will lead to the standard form of the hyperbola centered at the origin.Exploration 2.4.1: The Inverse of a Matrix In this quick Exploration, you are asked to find the inverse of matrix A where: O 2 1100 A = 3 010 4 8 100 Of course, this should be done by hand. How might you check your answer? Challenge: Based on this example, can you provide some general informal justifica- tion for why this process works? NOTE: If it is not possible to obtain the identity matrix on the left side of the augmented matrix by using matrix row operations, then A" does not exist