1. Chapter 6 Review of Conics
The line D is called the directrix and the point F is called the focus
If vertex is (h,k):
(y-k)2 = 4a(x-h)
Focus: (h+a,k)
Directory: x=h-a
(y-k)2 = -4a(x-h)
Focus: (h-a,k)
Directrix: x=h+a
(x-h)2 = 4a(y-k)
Focus: (k, h+a)
Directrix: y = k-a
(x-h)2 = -4a(y-k)
Directrix: y = k+a
A circle is a special ellipse with a=b.
Major Axis
Major Axis
General Equation of a Conic:
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
Parabola if B2 – 4AC = 0
Ellipse (or circle) if B2- 4AC < 0
Hyperbola if B2 - 4AC > 0

2. APPLICATIONS OF PARABOLAS
If a light (or any other emitting source) is placed at the focus of a parabola, all the rays emanating from the light will reflect off the mirror in lines parallel to the axis of symmetry.
Conversely, suppose rays of light (or other signals) emanate from a distant source (e.g. satellite) so that they are essentially parallel. When these rays strike the surface of a parabolic mirror whose axis of symmetry is parallel to these rays, they are reflected into a single point at the focus.
Example 10
Satellite Dish
If we model the satellite dish as an upward facing parabola, the formula is
x2 = 4ay
Satellite dish
If we knew a point (x,y) on this parabola, we could solve for a. Use given information to find a point. Once we know a, we know the focus of a parabola in the form
x2 = 4ay is (0,a). Therefore the receiver would need to be a feet away.

3. Applications of Ellipses
Mean distance
Aphelion
Perihelion
Major Axis
Center
The orbit of a planet about the Sun is an ellipse and the location of the Sun is the focus of the ellipse.
p. 440 #77
The mean distance is 93 million miles so the length of the ellipse is 2 x 93 million = 186 million. The Aphelion is 94.5 million, so the Perihelion is 186 million – 94.5 million = 91.5 million miles.
The equation for the ellipse is
Recall that the vertices of a horizontal ellipse with center at the origin are on the major axis at the points (-a,0) and (a,0) where a is half the length of the ellipse (mean distance) and the foci are located at (-c,0) and (c,0).
Therefore, in this problem, a = 93 million = 93 x 106
c = distance from center to sun
= mean distance – perihelion = 93 million – 91.5 million = 1.5 million.

4. HOMEWORK
p.424 #5,9,13
p. 485 #77
P. 488 #6
10 POINTS EXTRA CREDIT!
p.487 Chapter Project #1