9.1-9.5 Flashcards
Standard form of a circle with center at origin
x2+y2=r2
Write an equation of circle with a point
Plug in x and y
Solve
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
Major axis
Longer axis
Contains Foci
Ends with vertices
Minor axis
Shorter axis
Contains covertices
A
B
C
In ellipses
A-vertices
B-covertices
C-foci
Horizontal major ellipse equation
X2/a2 + y2/b2= 1
Horizontal major ellipse vertices and covertices equation
Vertices (+- a,0)
Covertices (0,+-b)
A away
B away
Vertical major ellipse equation
X2/b2 + y2/a2= 1
Vertical major ellipse vertices and covertices
Vertices (0,+-a)
Covertices (+-b,0)
How to find foci of ellipse
C UNITs from the center on the major axis
c2=a2-b2
For ellipse A goes under
Which ever axis is the major axis
Distance formula
D=|(x-x)2 + (y-y)2
Midpoint formula
(x+x/2, y+y/2)
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
Directrix
The perpendicular line to parabola
Any point on a parabola is —– to focus point and directrix
Equal distance
X=y2 parabola
Opens to side
Y2=x parabola
Opens up
Equation for parabola open up/ down
X2=4py
Equation for open up/down
focus
Directrix
Axis of symmetry for
Focus (0,p)
Directrix y=-p
AS vertical (x=0)
Equation for parabola opens right /left
Y2=4px
Equation for open right/left
focus
Directrix
Axis of symmetry for
Focus (p,0)
Directrix x=-p
AS horizontal (y=0)
How to graph a parabola
Match up equation
Find focus
Directrix
Determine two points from table
Hyperbola number of points
5
2-foci
2-vertices
1-center
Equation of hyperbola at origin horizontal
X2/a2 - y2/b2= 1
Horizontal so x leads
Asymptotes for hyperbolas
Under y/ under x (x)
Ex y= 1/2x
Vertices for horizontal hyperbola
(+-a,0)
A away
Vertices for hyperbola vertical
(0,+-a)
A away
Foci for hyperbola
Foci lie on the transverse axis, c units from the center
C2=a2 + b2
Translated equations
Replace x with
(X-h)
Y with
(Y-k)
Circle translated information
Center (h,k)
Hyperbola translated information
Center (h,k)
Vertices a away center
Slope under y/ under x
Foci is c away center
Parabola translated information
Vertex (h,k)
P is distance between focus and vertex
Foci p distance from vertex
Directrix p opposite direction from vertex
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
Conic
A
B
C
A= Ax2 B= Bxy C= Cy2
To determine iconic use
Discriminate
B2-4ac
Conic is circle
B2-4ac < 0
B=0
A=C
Conic is ellipse
B2-4ac < 0
B doesn’t = 0
A doesn’t = C
Conic is a parabola
B2-4ac =0
Conic is a hyperbola
B2-4ac > 0
If B= 0
Each axis of conic is horizontal or vertical
Solve by square
Separate x and y
(B/2)2
Add what happens to one side to other
For parabola focus and directrix
Focus
P units away from vertex
Directrix p units away from vertex in opposite direction
X and y for ellipse
Don’t move
A is always biggest
X and y for hyperbola
X and y do more
A is always first
