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