Conic Sections Overview
BROUGHT TO YOU BY : HEATHER H
c/o Sanderson High School, Intro to College Math
Chapter 10.5, Conic Sections
CONIC SECTIONS INCLUDE THE FOLLOWING FIGURES:
|
CONIC SECTION |
STANDARD FORM OF EQUATION |
VARIATION OF GENERAL FORM OF CONIC EQUATIONS |
|
CIRCLE |
(X-H)2 + (Y-K)2 = R2 |
A = C |
|
PARABOLA |
(Y-K)2 = 4P(X-H) OR (X-H)2 = 4P(Y-K) |
EITHER A OR C IS ZERO |
|
ELLIPSE |
(x-h)2 + (y-k)2 = 1 a2 b2 OR (y-k)2 + (x-h)2 = 1 a2 b2 |
A AND C HAVE THE SAME SIGN, AND A IS NOT EQUAL TO C |
|
HYPERBOLA |
(x-h)2 - (y-k)2 = 1 a2 b2 OR (y-k)2 - (x-h)2 = 1 a2 b2 xy = k |
A AND C HAVE OPPOSITE SIGNS |
THERE ARE ALSO DEGENERATE CASES:
POINT LINE
INTERSECTING LINES
GENERAL EQUATION FOR CONIC SECTIONS:
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
(A, B, AND C ARE NOT ALL 0)
ECCENTRICITY: ANOTHER METHOD IN DEFINING CONIC EQUATIONS
E = C, where c = the distance from the center to the focus and a =
A the distance from the center to the vertex.
parabola: e = 1 circle/ellipse: e <1, e doesn't equal 1 hyperbola: e > 1
!!!Word Problem!!!
A satellite orbiting Earth follows an elliptical path with Earth at its center. The eccentricity of the orbit is 0.18, and the major axis is 11,513 miles long. Assume that the center of the ellipse is the origin and the foci lie on the x-axis, write an equation of the orbit of the satellite.
A=11513 =5756.5 b2 = a2 (1-e2) (h, k) = (0,0)
2 b2 = 33137292.25 (1-.182) x2 + y2 = 1
5756.52 = 33137292.25 b2 = 27172579.65 33137292.25 27172579.65
|
You will find men who want to be carried on the shoulders
of others, who think that the world owes them a living. They don't seem to
see that we must all lift together and pull together. |
| Responsibility - The quote is saying that we all have a responsibility, which is to take care of each other. If one person doesn't do what they are responsible for, the entire human society will fall apart. Therefore, everyone needs to do their part in society. |
http://www.futurehealth.org/responsibility.htm
http://ccins.camosun.bc.ca/~jbritton/jbconics.htm