Circles are formed when the plane is parallel to the cone (e.g. m=0).
An ellipse is formed when the slope of plane is greater than 0, but less than the slant of the cone.
Hyperbolas are formed when the slope of the plane is greater than the slant of the cone.
Parabolas is formed when the slope of the plane & the slant of the cone are the same.
In regards to how various conics are related, circles and ellipses are both closed curves and increase in size as the plane moves away from the origin (e.g. b increases). Similarly, hyperbolas and parabolas are both open curves, which extend to infinity. As well, the vertices of both hyperbolas and parabolas get rounder as the plane moves away from the origin. Note, however, hyperbolas approach their asymptotes where parabolas do not.
Probability Review
Converting Review
Solving Review
Graphing Review
Answer to the hole to #3 should be (3,-1/6)
Corrections:
11. Domain [0, infinity)
12. Vertical stretch by a factor of 6
Answers to Practice 13.2-13.3 Extra Practice
Answer Key to Solving Quadratic Equations
Choose any 12, must use each form at least 3 times
Hyperbolas - Section 8.2
Section 3.3 #17-21 odd, 22-25 all, 27
#22. Increasing (-inf, -3) U (3, inf)
Decreasing (-3,3)
#24. Increasing (-8, -3) U (3, 7ish)
Decreasing (-3,3)
In Class Practice