1. Chapter 9 Notes
Honors Pre-Calculus

2. 9.1 Intro to Conics EQUATION: EQUATIONS:
A Circle is the set of all points, in a plane, such that each point is equidistant from a given point, the center.
EQUATION:
A Parabola is the set of all points, in a plane, that are equidistant from a given point, the focus, and a given line, the directrix.
EQUATIONS:

3. 9.1 cont’d. PICTURES Opens up/down Opens left/right Vertex : (h,k)
Axis of Symmetry : x = h y = k
Focus: (h, y+p) (h+p, k)
Directrix: y = k – p x = h – p
p is the distance from the vertex to the focus or vertex to the directrix. (p is directional)
PICTURES

4. 9.1 Examples Find the Standard Form Equation for each Parabola:
1. V (2, 3) Focus (2, 5) 2. V (-1, 4) D: x = 1
Find Everything:
Equation:
Vertex:
Focus:
Directrix:

5. 9.2 Ellipses
An Ellipse is the set of all points, in a plane, such that the sum of each points’ distances from two fixed points, the foci, is constant.
Equations:
Center : (h, k)
Horizontal -Major Axis- Vertical
Vertical -Minor Axis- Horizontal
C is the distance from the Center to the Foci.
Length of Major Axis – 2a Length of Minor Axis – 2b

6. 9.3 Hyperbolas Equations:
A Hyperbola is the set of all points, in a plane, such that the difference of each points’ two distances from two fixed points, the foci, is constant.
Equations:
Center: (h,k)
Right/Left OPENS Up/Down
a is the distance from Center to vertices.
“box” method for graphing, asymptotes.
2 “parabolas”
Slopes of asymptotes:

7. 9.5 Parametric Equations Equations:
If f and g are continuous functions of t on an interval, I.
The set of ordered pairs (f(t), g(t)) is a plane curve, C.
Parametric Equations
t is the parameter
Equations:
Plot points in order of increasing values of t, you trace the curve in a specific direction. Orientation of the curve.
Examples:
Eliminating the Parameter
1.Solve for t in one eq.
2.Substitute into 2nd eq.
3.Rectangular Equation

8. Finding Parametric Equations:
9.5 cont’d.
Finding Parametric Equations:
Answers:

9. 9.6/9.7 Polar Coordinates & Polar Graphs
Directed distance
Directed angle r
Plot points and give three equivalent points.
Polar Axis
Coordinate Conversions
Rect. To Polar r y x
Polar to Rect,
P to R
R to P
Convert:

10. 9.6/9.7 cont’d. GRAPHS: Rose Curves Circle Line n is odd, n petals
n is even, 2n petals
a is the length of petals
Circles
Equation Conversion
Need to know when sin and cos are (1 or -1).
For sin, # petals = # of values.
For cos, # petals need 1 more value.