9.1-9.5

Question 1

Standard form of a circle with center at origin

Answer 1

x2+y2=r2

Question 2

Write an equation of circle with a point

Answer 2

Plug in x and y

Solve

Question 3

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

Answer 3

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

Question 4

Major axis

Answer 4

Longer axis
Contains Foci
Ends with vertices

Question 5

Minor axis

Answer 5

Shorter axis

Contains covertices

Question 6

A
B
C
In ellipses

Answer 6

A-vertices
B-covertices
C-foci

Question 7

Horizontal major ellipse equation

Answer 7

X2/a2 + y2/b2= 1

Question 8

Horizontal major ellipse vertices and covertices equation

Answer 8

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

Question 9

Vertical major ellipse equation

Answer 9

X2/b2 + y2/a2= 1

Question 10

Vertical major ellipse vertices and covertices

Answer 10

Vertices (0,+-a)

Covertices (+-b,0)

Question 11

How to find foci of ellipse

Answer 11

C UNITs from the center on the major axis

c2=a2-b2

Question 12

For ellipse A goes under

Answer 12

Which ever axis is the major axis

Question 13

Distance formula

Answer 13

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

Question 14

Midpoint formula

Answer 14

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

Question 15

To find a perpendicular busector

Answer 15

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

Question 16

Directrix

Answer 16

The perpendicular line to parabola

Question 17

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

Answer 17

Equal distance

Question 18

X=y2 parabola

Answer 18

Opens to side

Question 19

Y2=x parabola

Answer 19

Opens up

Question 20

Equation for parabola open up/ down

Answer 20

X2=4py

Question 21

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

Answer 21

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

Question 22

Equation for parabola opens right /left

Answer 22

Y2=4px

Question 23

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

Answer 23

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

Question 24

How to graph a parabola

Answer 24

Match up equation
Find focus
Directrix
Determine two points from table

Question 25

Hyperbola number of points

Answer 25

5 2-foci 2-vertices 1-center

Question 26

Equation of hyperbola at origin horizontal

Answer 26

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

Question 27

Asymptotes for hyperbolas

Answer 27

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

Question 28

Vertices for horizontal hyperbola

Answer 28

(+-a,0) | A away

Question 29

Vertices for hyperbola vertical

Answer 29

(0,+-a) | A away

Question 30

Foci for hyperbola

Answer 30

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

Question 31

Translated equations

Answer 31

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

Question 32

Circle translated information

Answer 32

Center (h,k)

Question 33

Hyperbola translated information

Answer 33

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

Question 34

Parabola translated information

Answer 34

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

Question 35

Ellipse translated information

Answer 35

``` 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 ```

Question 36

Conic A B C

Answer 36

``` A= Ax2 B= Bxy C= Cy2 ```

Question 37

To determine iconic use

Answer 37

Discriminate | B2-4ac

Question 38

Conic is circle

Answer 38

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

Question 39

Conic is ellipse

Answer 39

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

Question 40

Conic is a parabola

Answer 40

B2-4ac =0

Question 41

Conic is a hyperbola

Answer 41

B2-4ac > 0

Question 42

If B= 0

Answer 42

Each axis of conic is horizontal or vertical

Question 43

Solve by square

Answer 43

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

Question 44

For parabola focus and directrix

Answer 44

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

Question 45

X and y for ellipse

Answer 45

Don't move | A is always biggest

Question 46

X and y for hyperbola

Answer 46

X and y do more | A is always first