Parabola Parts

1
Equation of Ellipse (1)
Parabola Parts
Parabola (Up\Down)
Equation of Ellipse (2)
Parabola (Left\Right)
Hyperbola (Left Right)
Equation of Parabola (Vertex, Focus)
Hyperbola (Up Down)
Equation of Parabola (Vert, Direct)
Equation of Hyperbola (1)
Equation (Line tangent to circle at a point)
Equation of Hyperbola (2)
Ellipse (Tall)
Please report any errors ASAP by email to
sakim_at_fjuhsd.net or IM at kimtroymath. Problems
may be more difficult on test. Consult homework
assignment. Not all topics covered.
Ellipse (Wide)
2
Up\down parabola Right (pos)\Left(neg) parabola
Vertex Focus Directrix Axis of Symmetry
How to graph 1) Opens 2) Vertex, aos 3) Find
p 4) Focus 5) Directrix
Focus On a.o.s., is inside the
parabola Directrix perpendicular to a.o.s, is
outside the parabola All points on the parabola
are equidistant from the focus and the directrix
6) Latus Rectum 4p through focus
3
How to graph 1) Opens 2) Vertex\aos 3) Find
p 4) Focus 5) Directrix
Down
(3, 4) x 3
p -2
(3, 4 (-2)) (3, 2)
x 3
y 6
y 4 (-2) ? y 6
(3, 4)
Latus Rectum
4p 8
(3, 2)
Dont have to necessarily memorize, just think
about these.
4
1) Opens 2) Vertex, aos 3) Find p 4)
Focus 5) Directrix
Right
(-5,-2), y -2
(-5,-2)
y -2
Latus Rectum
4p 1\2
Dont have to necessarily memorize, just think
about these.
5
Equation of parabola given vertex and focus.
Vertex (2,1) Focus (4,1)
1) Opening 2) Vertex 3) Find p 4) Plug in parts
6
Equation of parabola given vertex and directrix.
Vertex (2,-3) Directrix y
1) Opening 2) Vertex 3) Find p 4) Plug in parts
7
Equation of tangent line given center, point

• Find center
• Other point
• 2) Find slope
• 3) Perp Slope
• 4) Eq of line

(3, -1)
(x - 3)2 (y 1)2 20
(5, 3)
(5,3) is point on circle
8

• 1) Tall or Wide?
• 2) Find center
• Find a and plot
• Find b and plot
• Find c and plot

9

• 1) Tall or Wide?
• 2) Find center
• Find a and plot
• Find b and plot
• Find c and plot

10
NOTE If you have a and b, you dont need c
Vertices (4,0), (-2,0) Foci
(2,0), (0,0)
1 Find Center 2 Tall or Wide 3 Find a
b c 4 Find what you
dont have 5 Plug it in
11
NOTE If you have a and b, you dont need c
Co-Vertices (5,-1), (-3,-1)
Foci (1,8), (1,-10)
1 Find Center 2 Tall or Wide 3 Find a
b c 4 Find what you
dont have 5 Plug it in
12
Steps 1 Find Center 2 Find a and plot 3
Find b and plot 4 Make box and sketch
asymptotes 5 Find c, foci 6 Sketch 7
Equation of asymptotes
13
Steps 1 Find Center 2 Find a and plot 3
Find b and plot 4 Make box and sketch
asymptotes 5 Find c, foci 6 Sketch 7
Equation of asymptotes
14
Vertices (4,0), (-2,0) Foci
(5,0), (-3,0)
1 Find Center 2 Up\Down, or Left\Right 3
Find a b c 4
Find what you dont have 5 Plug it in
15
Vertices (1,-3), (1,5) Foci
(1,-5), (1,7)
1 Find Center 2 Up\Down, or Left\Right 3
Find a b c 4
Find what you dont have 5 Plug it in
16
(No Transcript)