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Algebra 2 > 9.1-9.5 > Flashcards

9.1-9.5 Flashcards

1
Q

Standard form of a circle with center at origin

A

x2+y2=r2

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2
Q

Write an equation of circle with a point

A

Plug in x and y

Solve

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3
Q

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

A

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

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4
Q

Major axis

A

Longer axis
Contains Foci
Ends with vertices

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5
Q

Minor axis

A

Shorter axis

Contains covertices

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6
Q

A
B
C
In ellipses

A

A-vertices
B-covertices
C-foci

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7
Q

Horizontal major ellipse equation

A

X2/a2 + y2/b2= 1

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8
Q

Horizontal major ellipse vertices and covertices equation

A

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

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9
Q

Vertical major ellipse equation

A

X2/b2 + y2/a2= 1

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10
Q

Vertical major ellipse vertices and covertices

A

Vertices (0,+-a)

Covertices (+-b,0)

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11
Q

How to find foci of ellipse

A

C UNITs from the center on the major axis

c2=a2-b2

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12
Q

For ellipse A goes under

A

Which ever axis is the major axis

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13
Q

Distance formula

A

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

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14
Q

Midpoint formula

A

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

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15
Q

To find a perpendicular busector

A

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

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16
Q

Directrix

A

The perpendicular line to parabola

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17
Q

Any point on a parabola is —– to focus point and directrix

A

Equal distance

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18
Q

X=y2 parabola

A

Opens to side

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19
Q

Y2=x parabola

A

Opens up

20
Q

Equation for parabola open up/ down

A

X2=4py

21
Q

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

A

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

22
Q

Equation for parabola opens right /left

A

Y2=4px

23
Q

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

A

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

24
Q

How to graph a parabola

A

Match up equation
Find focus
Directrix
Determine two points from table

25
Q

Hyperbola number of points

A

5
2-foci
2-vertices
1-center

26
Q

Equation of hyperbola at origin horizontal

A

X2/a2 - y2/b2= 1

Horizontal so x leads

27
Q

Asymptotes for hyperbolas

A

Under y/ under x (x)

Ex y= 1/2x

28
Q

Vertices for horizontal hyperbola

A

(+-a,0)

A away

29
Q

Vertices for hyperbola vertical

A

(0,+-a)

A away

30
Q

Foci for hyperbola

A

Foci lie on the transverse axis, c units from the center

C2=a2 + b2

31
Q

Translated equations

A

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

32
Q

Circle translated information

A

Center (h,k)

33
Q

Hyperbola translated information

A

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

34
Q

Parabola translated information

A

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

35
Q

Ellipse translated information

A 
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
Q

Conic
A
B
C

A 
A= Ax2
B= Bxy
C= Cy2
37
Q

To determine iconic use

A

Discriminate

B2-4ac

38
Q

Conic is circle

A

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

39
Q

Conic is ellipse

A

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

40
Q

Conic is a parabola

A

B2-4ac =0

41
Q

Conic is a hyperbola

A

B2-4ac > 0

42
Q

If B= 0

A

Each axis of conic is horizontal or vertical

43
Q

Solve by square

A

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

44
Q

For parabola focus and directrix

A

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

45
Q

X and y for ellipse

A

Don’t move

A is always biggest

46
Q

X and y for hyperbola

A

X and y do more

A is always first

Algebra 2 (28 decks)

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