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Flashcards in 9.1-9.5 Deck (46):
1

Standard form of a circle with center at origin

x2+y2=r2

2

Write an equation of circle with a point

Plug in x and y
Solve

3

Steps to write an equation of a line tangent to the circle

Find slope of radius to point, (0,0) to point
Find slope of tangent (radical of slope)
Use point slope form to find the equation of the tangent line or y=mx+b

4

Major axis

Longer axis
Contains Foci
Ends with vertices

5

Minor axis

Shorter axis
Contains covertices

6

A
B
C
In ellipses

A-vertices
B-covertices
C-foci

7

Horizontal major ellipse equation

X2/a2 + y2/b2= 1

8

Horizontal major ellipse vertices and covertices equation

Vertices (+- a,0)
Covertices (0,+-b)
A away
B away

9

Vertical major ellipse equation

X2/b2 + y2/a2= 1

10

Vertical major ellipse vertices and covertices

Vertices (0,+-a)
Covertices (+-b,0)

11

How to find foci of ellipse

C UNITs from the center on the major axis
c2=a2-b2

12

For ellipse A goes under

Which ever axis is the major axis

13

Distance formula

D=\|(x-x)2 + (y-y)2

14

Midpoint formula

(x+x/2, y+y/2)

15

To find a perpendicular busector

Find midpoint of segment
Find the slope of segment
Find slope of perpendicular line
Use y=mx+b to form equation with perpendicular slope and midpoint

16

Directrix

The perpendicular line to parabola

17

Any point on a parabola is ----- to focus point and directrix

Equal distance

18

X=y2 parabola

Opens to side

19

Y2=x parabola

Opens up

20

Equation for parabola open up/ down

X2=4py

21

Equation for open up/down
focus
Directrix
Axis of symmetry for

Focus (0,p)
Directrix y=-p
AS vertical (x=0)

22

Equation for parabola opens right /left

Y2=4px

23

Equation for open right/left
focus
Directrix
Axis of symmetry for

Focus (p,0)
Directrix x=-p
AS horizontal (y=0)

24

How to graph a parabola

Match up equation
Find focus
Directrix
Determine two points from table

25

Hyperbola number of points

5
2-foci
2-vertices
1-center

26

Equation of hyperbola at origin horizontal

X2/a2 - y2/b2= 1
Horizontal so x leads

27

Asymptotes for hyperbolas

Under y/ under x (x)
Ex y= 1/2x

28

Vertices for horizontal hyperbola

(+-a,0)
A away

29

Vertices for hyperbola vertical

(0,+-a)
A away

30

Foci for hyperbola

Foci lie on the transverse axis, c units from the center
C2=a2 + b2

31

Translated equations

Replace x with
(X-h)
Y with
(Y-k)

32

Circle translated information

Center (h,k)

33

Hyperbola translated information

Center (h,k)
Vertices a away center
Slope under y/ under x
Foci is c away center

34

Parabola translated information

Vertex (h,k)
P is distance between focus and vertex
Foci p distance from vertex
Directrix p opposite direction from vertex

35

Ellipse translated information

Center (h,k)
Center is midpoint between Foci
B distance between covertices/2
Plug into c2=a2-b2
Co vertices b away
Foci is c away

36

Conic
A
B
C

A= Ax2
B= Bxy
C= Cy2

37

To determine iconic use

Discriminate
B2-4ac

38

Conic is circle

B2-4ac < 0
B=0
A=C

39

Conic is ellipse

B2-4ac < 0
B doesn't = 0
A doesn't = C

40

Conic is a parabola

B2-4ac =0

41

Conic is a hyperbola

B2-4ac > 0

42

If B= 0

Each axis of conic is horizontal or vertical

43

Solve by square

Separate x and y
(B/2)2
Add what happens to one side to other

44

For parabola focus and directrix

Focus
P units away from vertex
Directrix p units away from vertex in opposite direction

45

X and y for ellipse

Don't move
A is always biggest

46

X and y for hyperbola

X and y do more
A is always first