Download presentation

Presentation is loading. Please wait.

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.

Similar presentations

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google