Download Day 4 - Graphing Parabolas

Warm-up!!
Draw the circle (use graph page) and give the center and radius.
1. ( x  2) 2  ( y  3) 2  36
Write an equation of a circle passing through the given point
and has a center at the origin.
2. ( 8, 6)
Write an equation of a tangent line to the given circle:
3. x 2  y 2  13 ; (3, 2)
Write the equation of the circle in standard form.
State the Center and Radius
4. x 2  y 2  14 x  2 y  49  0
Parabolas
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.
The cross section of a headlight
is an example of a parabola...
Directrix
The light
source is the
Focus
Here are some other applications of the
parabola...
d2
d1Focus
d3
d1
Vertex d3
d2
Directrix
Notice that the vertex is located at the midpoint between the focus
and the directrix...
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....
Standard Equation of a Parabola: (Vertex at the origin)
Equation
2
(x-h) = 4p(y-k)
Focus
(h, k+p)
Directrix
y = k–p
(If the x term is squared, the parabola
is up or down)
Equation
2
(y-k) = 4p(x-h)
Focus
(h+p, k)
Directrix
x = h–p
(If the y term is squared, the parabola is
left or right)
Tell whether the parabola opens
up down, left, or right.
A.
2
y 5x
B.
2 y 2  8x
right
C.
4x  y2
left
down
Find the focus and equation of the
directrix. Then sketch the graph.
4 p  16
p4
1. y  16 x
2
 0,0
Focus :  4, 0 
Vertex :
Directrix :
P= 4
x  4
Direction: Opens right
Find the focus and equation of the
directrix. Then sketch the graph.
4p  2
1
p
2
2. x  2 y
2
Vertex :
 0,0
1

Focus :  0, 
 2
P= 1/2
1
Directrix : y  
2
Direction: Opens right
Find the focus and equation of the
directrix. Then sketch the graph.
4 p  12
p  3
3. x  12 y
2
 0,0
Focus : 0, 3
Vertex :
Directrix :
P= -3
y3
Direction: Opens down
Find the focus and equation of the
directrix. Then sketch the graph.
4.  3 y  12 x  0
2
 0,0
Focus : 1,0 
Vertex :
Directrix :
x 1
4 p  4
p  1
P= -1
Direction: Opens left
Find the focus and equation of the
directrix. Then sketch the graph.
4 p  16
5: (y – 2) = -16 (x - 5)
p  4
2
5,2
Focus : 1,2 
Vertex :
Directrix :
P= -4
x9
Direction: Opens left
Find the focus and equation of the
directrix. Then sketch the graph.
4p  8
p2
6. (x – 8)2 = 8(y + 3)
8, 3
Focus :8, 1
Vertex :
Directrix :
P= 2
y  5
Direction: Opens up
Writing Equations
of Parabolas
In
Standard Form
7. Write the equation in standard form by
completing the square.
State the VERTEX & DIRECTION.
2
x  2 x  8y  17  0
7. 8. Write the equation in standard form
by completing the square.
State the VERTEX & DIRECTION.
2
y  6y  2x  9  0
YOU TRY # 7 & #8
2
7. y  4y  2 x  2  0
2
8. x  8 x  4y  4  0