Elipse
Circle
Hyperbola
Parabola
Section 8.1: Midpoint & Distance Formulas
What does the midpoint formula do & why is it useful?
•Midpoint formula allows you to find the middle of something as an EXACT POINT
A
B
Midpoint – Half Way
Section 8.1: Midpoint & Distance Formulas
Midpoint
1 1( , )x y
2 2( , )x y1 2 1 2,
2 2x x y y
Section 8.1: Midpoint & Distance Formulas
What does the distance formula do & why is it useful?
•Distance formula allows you to find the length of something as an EXACT VALUE
A
B
How long is the linefrom point A to point B?
Section 8.1: Midpoint & Distance Formulas
1 1,x y
2 2,x y
2 1x x
2 1y y
How does this help with the distance of the line?
* Ask Pythagoras: 2 2 2a b c
A
B
C
Section 8.1: Midpoint & Distance Formulas
1 1,x y
2 2,x y
2 1x x
2 1y yA
B
This gives the Distance Formula:
2 22 1 2 1( )d x x y y
Section 8.1: Midpoint & Distance Formulas
End Day #1
Homework:
Pg. 414 ( 13 – 19 odd, 25 – 31 odd, 34, 35, 43, 44 )
Section 8.2: Parabolas
What should we remember from chapter 6?
•Standard form of the equation of a Parabola
•How a Vertex is written
•How to tell if the parabola opens up or down
2( )y a x h k
( , )h k
If a > 0, parabola opens upIf a < 0, parabola opens down
Section 8.2: Parabolas
Does the parabola always open up or down?
-- No, it can also open left or right
Section 8.2: Parabolas
Table of Concept Summary for Parabolas
Form of Equation
Vertex (h, k) (h, k)
Axis of Symmetry x = h y = k
Focus
Directrix
Direction of Opening Up, if a > 0Down, if a < 0
Right, if a > 0Left, if a < 0
2( )y a x h k 2( )x a y k h
1,4
h ka
1 ,4
h ka
14
y ka
14
x ha
Section 8.2: Parabolas
End Day #2
Homework:
Pg. 424 ( 12 – 14, 16 – 18, 21 – 23, 25, 30 – 34, 48, 49 )
Directions for (16 – 18, 21 – 23, 25):
Write each equation in standard form.
Find vertex, axis of symmetry,y-intercept if y= and
x-intercept if x=, tell the direction of opening, and graph.
Section 8.3: Circles
How do write out the equation of a circle with center at (0,0)? 2 2 2x y r
What is r? r is the radius, which is the distance from the center of the circle to the edge
What if center is not (0,0)? new center is written as (h,k)and we use the formula
2 2 2( ) ( )x h y k r
Section 8.3: Circles
What if we are given two points and need to find the equation of the circle? 1 1,x y
2 2,x y
1. Use Midpoint Formula- this gives the center (h,k)
2. Use Distance Formula- this gives the radius length (r)
3. Plug values into general equation.
Section 8.3: Circles
What if we are given the center and a tangent?
1. Substiute in the center (h,k) and point that is tangent (x,y) into general equation
2. Solve for radius (r)
3. Plug center (h,k) and radius (r) into general equation.
(x, y)
(h,k)
Section 8.3: Circles
End Day #3
Homework:
Pg. 429 ( 17 – 25 odd, 28, 29 – 45 odd )
Section 8.4: Ellipses
X-axis
Y-axis
(-a,0) (a,0)
F (-c,0) F (c,0)
baa
Major Axis
MinorAxis
Section 8.4: Ellipses
Table of Information for Ellipses with center at Origin (0,0):
Standard Form of Equation
Direction of Major Axis
Horizontal Vertical
Foci (c, 0) & (-c, 0) (0, c) & (0, -c)
Length ofMajor Axis
2a 2a
Length ofMinor Axis
2b 2b
2 2
2 2 1x ya b
2 2
2 2 1y xa b
Section 8.4: Ellipses
What Changes if Ellipse is not centered on the origin?
Standard Form of Equation
Foci
2 2
2 2
( ) ( ) 1x h y ka b
2 2
2 2
( ) ( ) 1y k x ha b
( , )h c k ( , )h k c
Section 8.4: Ellipses
End Day #4
Homework:
Pg. 438 (13 – 19 odd, 22, 24 – 35 Left Hand Column, do not worry about Foci)
Section 8.5: Hyperbolas
What are Hyperbolas? * Hyperbolas can be thought of as two parabolas going in opposite directions
Section 8.5: Hyperbolas
Table of Information about HyperbolasCentered at Origin
Standard Form of Equation
Direction of Transverse Axis
Horizontal Vertical
Vertices ( a, 0 ) & ( -a, 0 ) ( 0, a ) & ( 0, -a )
Equations of Asymptotes
2 2
2 2 1x ya b
2 2
2 2 1y xa b
by xa
ay xb
Section 8.5: Hyperbolas
a
b
by xa
Section 8.5: Hyperbolas
What Changes when Hyperbola is NOT Centered at the Origin
Standard Form of Equation
Equations of Asymptotes
2 2
2 2
( ) ( ) 1x h y ka b
2 2
2 2
( ) ( ) 1y k x ha b
( )by k x ha
( )ay k x hb
Section 8.5: Hyperbolas
Homework:Pg. 445 – 6 – 8: graph, give coordinates of vertices, & equations of asymptotes
21 – 31 odd: do NOT find the foci
41, 42
End Day #5
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