Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics

1. Elipse
Circle
Hyperbola
Parabola

2. 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

3. Section 8.1:
Midpoint & Distance Formulas
Midpoint
1 1( , )x y
2 2( , )x y
1 2 1 2
,
2 2
x x y y+ + 
 ÷
 

4. 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 line
from point A to point B?

5. 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 2
a b c+ =
A
B
C

6. Section 8.1:
Midpoint & Distance Formulas
( )1 1,x y
( )2 2,x y
2 1x x−
2 1y y−A
B
This gives the Distance Formula:
( )
2 2
2 1 2 1( )d x x y y= − + −

7. Section 8.1:
Midpoint & Distance Formulas
End Day #1
Homework:
Pg. 414 ( 13 – 19 odd, 25 – 31 odd, 34, 35, 43, 44 )

8. 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 up
If a < 0, parabola opens down

9. Section 8.2:
Parabolas
Does the parabola always open up or down?
-- No, it can also open left or right

10. 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 > 0
Down, if a < 0
Right, if a > 0
Left, if a < 0
2
( )y a x h k= − + 2
( )x a y k h= − +
1
,
4
h k
a
 
+ ÷
 
1
,
4
h k
a
 
+ ÷
 
1
4
y k
a
= −
1
4
x h
a
= −

11. 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.

12. Section 8.3:
Circles
How do write out the equation of a circle
with center at (0,0)? 2 2 2
x 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− + − =

13. 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.

14. 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)

15. Section 8.3:
Circles
End Day #3
Homework:
Pg. 429 ( 17 – 25 odd, 28, 29 – 45 odd )

16. Section 8.4:
Ellipses
X-axis
Y-axis
(-a,0) (a,0)
F (-c,0) F (c,0)
b
aa
Majo
r Axis
Minor
Axis

17. 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 of
Major Axis
2a 2a
Length of
Minor Axis
2b 2b
2 2
2 2
1
x y
a b
+ =
2 2
2 2
1
y x
a b
+ =

18. Section 8.4:
Ellipses
What Changes if Ellipse is not centered on the origin?
Standard Form
of Equation
Foci
2 2
2 2
( ) ( )
1
x h y k
a b
− −
+ =
2 2
2 2
( ) ( )
1
y k x h
a b
− −
+ =
( , )h c k± ( , )h k c±

19. Section 8.4:
Ellipses
End Day #4
Homework:
Pg. 438 (13 – 19 odd, 22, 24 – 35 Left Hand
Column, do not worry about Foci)

20. Section 8.5:
Hyperbolas
What are Hyperbolas?
* Hyperbolas can be thought of as two parabolas
going in opposite directions

21. Section 8.5:
Hyperbolas
Table of Information about Hyperbolas
Centered 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
1
x y
a b
− =
2 2
2 2
1
y x
a b
− =
b
y x
a
= ± a
y x
b
= ±

22. Section 8.5:
Hyperbolas
a
b
b
y x
a
= ±

23. 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
( ) ( )
1
x h y k
a b
− −
− =
2 2
2 2
( ) ( )
1
y k x h
a b
− −
− =
( )
b
y k x h
a
− = ± − ( )
a
y k x h
b
− = ± −

24. 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