Ch. 10 Conics
10.1 Lines
A. OBJ: Find the inclination of a line. Find the angle between two lines. Find the distance between a point and a line.
B. FACTS:
1. Inclination of a line:
2. Angle between 2 lines: When two distinct lines intersect and are nonperpendicular, their intersection forms two pairs of opposite angles. One pair is acute and the other pair is obtuse. The smaller of these angles is the angle between the two lines. If two lines have inclinations

1
and

2
, where

1
 
2
and

2
–

1
 
/2, then the angle between the two lines is

=

2
–

1
.

tan

= tan(

2
–

1
)
3. Distance between a pt. and a line:

10.2 Parabolas
A. OBJ: Recognize a conic as the intersection of a plane and a double-napped cone.
Write equations of parabolas in standard form.
B. FACTS:
1. A conic section (or simply conic) is the intersection of a plane and a doublenapped cone.
Circle
2. Parabola:
Ellipse Parabola Hyperbola

( x – h )
2
= 4 p ( y – k )
Vertical axis: p  0
( y – k )
2
= 4 p ( x – h )
Horizontal axis: p  0

10.3 Ellipse
A. OBJ: Write equations of ellipses in standard form and graph ellipses.
B. FACTS:
1. Ellipse: d
1
+ d
2
is constant.
2. Properties of an Ellipse: The line through the foci intersects the ellipse at two points called vertices. The chord joining the vertices is the major axis, and its midpoint is the center of the ellipse. The chord perpendicular to the major axis at the center is the minor axis of the ellipse.

a.
An ellipse is the set of all points P in a plane such that the sum of the distances between P and two fixed points, called the foci , is a constant. b.
The line through the foci intersects the ellipse at two vertices.
The major axis joins the vertices. Its midpoint is the ellipse's center.
c.
The line perpendicular to the major axis at the center intersects the ellipse at the two co-vertices, which are joined by the minor axis.

10.4 Graph and Write equations of Hyperbolas
A.OBJ: to graph and write equations of hyperbolas
B.Facts/Formulas:
1.
A hyperbola is the set of all points P in a plane such that the difference of the distances between P and two fixed points, again called the foci, is a constant.
2.
The line through the foci intersects the hyperbola at the two vertices.
The transverse axis joins the vertices. Its midpoint is the hyperbola's
center.
Transverse axis is horizontal.
Transverse axis is vertical.

3.
Transformations: