Amy's Reflection #7

Ellipses

Steps:

1. find the center
2. determine the major axis
3. find the vertex (± √big denom)
4. find the other intercept ( ± √small denom)
5. find the focus (c^2 = a^2 + b^2)
6. determine the length of the major axis (2√big denom)
7. find the length of the minor axis (2√small denom)
8. finally graph

Example 1: Graph the following ellipse. Find its major intercepts, length of the major axis, minor intercepts, length of the minor axis, and foci.

x^2/4 + y^2/9 = 1

This ellipse is centered at (0, 0). Since the larger denominator is with the y variable, the major axis lies along the y-axis.

Since a^2 = 9 then a = 3 & Since b^2 = 4 then b = 2

Major intercepts: (0, 3), (0, –3)

Length of major axis: 2 √9 = 6

Minor intercepts: (2, 0), (–2, 0)

Length of minor axis: 2√4 = 4

c^2 = a^2 + b^2

= 9 - 4

= 5

= √5

Foci: (0, √5) , (0, -√5)

then you graph your points..

ok im also having some problems with hyperbolas..i know how to do #s 1-6 from the homework. i mean that's easy; all you got to do is follow your notes, but i dont know how to #s 7 & 8. if anyone can help me with those two problems, i'll be really greatful..