Post on 23-Dec-2015
transcript
2 2
Write an equation of a circle passing thr
Draw the circle (rough sketch) and give the
ough the given point
and has a center at th
1
e
.
Write the equa
origi
( 2) ( 3) 36
2. ( 8,6)
center and
n
ti
radius.
.
on
x y
2 2
of the circle in standard form.
State the Ce
3.
nter and
14 2 49 0
Radi
us
x y x y
Warm-up!!
CCGPS GeometryDay 60 (11-5-13)
UNIT QUESTION: How are the equations of circles and parabolas derived?Standard: MCC9-12..A.REI.7, G.GPE.1,2 and 4
Today’s Question:How do we graph a parabola from a given equation in standard form?Standard: MCC9-12..G.GPE.2
Parabolas
Parabola: the set of points in a plane that are the same distance from a given point called the focus and a given line called the directrix.
Directrix
The light source is theFocus
The cross section of a headlightis an example of a parabola...
Directrix
Focus
d1
d1
d2
d2
d3
d3
Also, notice that the distance from the focus to any point on the parabola is equal to the distance from that point to the directrix...
We can determine the coordinates of the focus, and the equation of the directrix, given the equation of the parabola....
Vertex
Notice that the vertex is located at the midpoint between the focusand the directrix...
Standard Equation of a Parabola: (Vertex at the origin)
Equation Focus Directrix
x2 = 4py (0, p) y = –p
Equation Focus Directrix
y2 = 4px (p, 0) x = –p
(If the x term is squared, the parabola is up or down)
(If the y term is squared, the parabola isleft or right)
Tell whether the parabola opens up down, left, or right.
2
2
2
. 5
2 8
. 4
.
A
B y x
x
C y
y
x
down
right
left
Find the focus and equation of the directrix. Then sketch the graph.
21. 16y x
: ,0Focus p 4 16p
4,0
4p
:Directrix x p
4x
Opens right
Find the focus and equation of the directrix. Then sketch the graph.
22. 2x y : 0,Focus p
4 2p 1
0,2
1
2p
:Directrix y p1
2y
Opens up
Find the focus and equation of the directrix. Then sketch the graph.
23. 12x y
: 0,Focus p4 12p
0, 3
3p
:Directrix y p
3y
Opens down
Find the focus and equation of the directrix. Then sketch the graph.
24. 3 12 0 y x
: 0,Focus p4 4p
1,0
1p
:Directrix y p
1x
Opens left
Example 5: Determine the focus and directrix of the parabola (y – 2)2 = -16 (x - 5) :
Direction:
Vertex:
Focus:
Directrix:
Example 6: Determine the focus and directrix of the parabola (x – 6)2 = 8(y + 3) :
Direction:
Vertex:
Focus:
Directrix: