Student’s Name: Osama Zaid AL MENHALI 1011090131
Saeed Zaid AL MENHALI 1011090130
Abdullah Khamis AL AMERI 1011090072
Section: 12 -03
2011 - 2012

Part I:
The figure below shows the graph of a parabola.
A (3 , 4.5)

1.
Plot the point A (3, 4.5), and draw the straight line (

) with equation 𝑦 = −
1
2 on the same graph above.
2.
Calculate the distance between the points A and S (0, 0.5).
A (3 , 4.5) S (0 , 0.5) d= √(𝒙𝑨 − 𝒙𝑺) 𝟐 + (𝒚𝑨 − 𝒚𝑺) 𝟐
= √(𝟑 − 𝟎) 𝟐 + (𝟒. 𝟓 − 𝟎. 𝟓) 𝟐 = 𝟓
3. Find the distance between the point A and the straight line (

). d= √(𝒙𝑨 − 𝒙
 ) 𝟐 + (𝒚𝑩 − 𝒚
 ) 𝟐 = √(𝟑 − 𝟑) 𝟐 + (𝟒. 𝟓 + 𝟎. 𝟓) 𝟐 = 𝟓
4. Compare the distances found in 2 and 3 . d
2
=d
3
5=5
5.
What is the name of the: i.
Point S: Focus ii.
Straight line (

): Directrix
2

Generalization:
Let 𝑃(𝑥, 𝑦) is a point of the drawn parabola, and 𝐹(0, 𝑝) the focus point of the parabola ( 𝑝 > 0 ) as illustrated in the figure below.
6.
Find the distance d
1
between P and F, and the distance d
2
between P and the straight line with equation 𝑦 = −𝑝 d
1
= √(𝒙𝑭 − 𝒙𝑷) 𝟐 + (𝒚𝑭 − 𝒚𝑷) 𝟐
= √(𝟎 − 𝒙) 𝟐 + (𝒑 − 𝒚) 𝟐 = 𝒙 + 𝑷 − 𝒚 d
2
= √(𝒙 − 𝒙) 𝟐 + (𝒚 + 𝒑) 𝟐 = 𝒚 + 𝒑
7.
Find the relation between x and y when d
1
= d
2
. 𝒙 + 𝑷 − 𝒚 = 𝒚 + 𝒑 𝒙 = 𝟐𝒚
3

Application
8.
A cross-section of a parabolic reflector is shown in the figure.
The bulb is located at the focus and the opening at the focus is 10 cm y x i.
Find an equation of the parabola.
V (0 , 0) latus rectum = |
𝟏
𝑨
𝟏
| = 𝟏𝟎 a=
𝟏𝟎 𝒙 = 𝒂(𝒚 − 𝒌) 𝟐 + 𝒉 =
𝟏
𝟏𝟎
(𝒚) 𝟐 ii.
Find the diameter of the opening |CD|, 11 cm from the vertex. 𝒙 =
𝟏
𝟏𝟎
(𝒚) 𝟐
𝟏𝟏 =
𝟏
𝟏𝟎
(𝒚) 𝟐 𝒚 = ±√𝟏𝟏𝟎 𝑪(𝟏𝟏 , √𝟏𝟏𝟎) 𝑫(𝟏𝟏 , −√𝟏𝟏𝟎) d=
√(𝟏𝟏 − 𝟏𝟏) 𝟐 + (−√𝟏𝟏𝟎 − √𝟏𝟏𝟎)
𝟐
= 𝟐√𝟏𝟏𝟎 𝒄𝒎
4

Part II
In the LORAN ( LO ng RA nge N avigation) radio navigation system, two radio stations located at A and B transmit simultaneous signals to a ship located at P.
The onboard computer converts the time difference in receiving these signals into a distance difference |PA|

|PB|, and this, according to the definition of a hyperbola, locates the ship on one branch of a hyperbola (see the figure).
Suppose that station B is located 400 mi due east of station A on a coastline.
A ship received the signal from B 1200 microseconds (
 s) before it received the signal from A.
(a) Assuming that radio signals travel at a speed of 980 ft/  s, find an equation of the hyperbola on which the ship lies.
Lets F
A
(-200 , 0) & F
B
(200 , 0) so c = 200 mi
||𝑨𝑷| − |𝑩𝑷|| = (𝟏𝟐𝟎𝟎 × 𝟗𝟖𝟎) = 𝟏𝟏𝟕𝟔𝟎𝟎𝟎 𝒇𝒕 =
𝟐𝟒𝟓𝟎
𝒎𝒊
𝟏𝟏
||𝑨𝑷| − |𝑩𝑷|| = 𝟐𝒂
𝟐𝒂 = 𝒃
𝟐
𝟐𝟒𝟓𝟎
= 𝒄 𝒙
𝟐
𝟐
𝟏𝟏
− 𝒂
𝟏𝟐𝟒𝟎𝟏.𝟖𝟓𝟗𝟓
−
𝒎𝒊 𝒂 =
𝟐
= 𝟒𝟎𝟎𝟎𝟎 − (
𝟏𝟐𝟐𝟓
𝟏𝟏 𝒚
𝟐
= 𝟏
)
𝟐
𝟐𝟔𝟓𝟗𝟖.𝟏𝟒𝟎𝟓
𝟏𝟐𝟐𝟓
𝟏𝟏
𝒎𝒊
= 𝟐𝟔𝟓𝟗𝟖. 𝟏𝟒𝟎𝟓
5

(b) If the ship is due north of B, how far of the coastline is the ship? 𝒙
𝟐
𝟏𝟐𝟒𝟎𝟏.𝟖𝟓𝟗𝟓
− 𝒚
𝟐
𝟐𝟔𝟓𝟗𝟖.𝟏𝟒𝟎𝟓
= 𝟏
(𝟐𝟎𝟎) 𝟐
𝟏𝟐𝟒𝟎𝟏.𝟖𝟓𝟗𝟓
− 𝒚 𝟐
𝟐𝟔𝟓𝟗𝟖.𝟏𝟒𝟎𝟓
= 𝟏 𝒚 𝟐
−
𝟐𝟔𝟓𝟗𝟖.𝟏𝟒𝟎𝟓
= 𝟏 −
(𝟐𝟎𝟎) 𝟐
𝟏𝟐𝟒𝟎𝟏.𝟖𝟓𝟗𝟓 𝒚
𝟐
−
𝟐𝟔𝟓𝟗𝟖. 𝟏𝟒𝟎𝟓
= −𝟐. 𝟐𝟐𝟓𝟑𝟐𝟐𝟕𝟖𝟑 𝒚 = √ (−𝟐𝟔𝟓𝟗𝟖. 𝟏𝟒𝟎𝟓)(−𝟐. 𝟐𝟐𝟓𝟑𝟐𝟐𝟕𝟖𝟑) = 𝟐𝟒𝟑. 𝟐𝟖𝟖𝟖𝟏𝟔𝟏 𝒎𝒊
6

4 3
Criteria
2 1
Points
Completeness of
Tasks
20%
Tasks are totally completed and correct. (100%)
Tasks are partially completed,
OR
Partially wrong.(75%)
Tasks are partially completed,
AND
Partially wrong
(50%).
Tasks are
Attempted (25% or less)
____
Presentation and
Integration of
Technology
70%
Students used one mean of technology.
The tool used helped the student and was useful to support his project.
Moreover, the student was able to explain the work he/she submitted confidently and fluently; he/she was
able to answer all of colleagues and instructor’s questions
Student used a mean of technology but it was not that supportive to the topic. In addition, student was able to explain the work he/she submitted confidently and fluently and he/she reflected an understanding of his/her works. The student was able to
answer most of colleagues and instructor’s questions.
Student was able to explain the work he/she submitted.
Student reflected a shallow understanding of his/her work; she was able to
answer some of colleagues and instructor’s questions,
Student use of technology was primitive and way below the level of other IAT students.
Student was unable to explain the work he/she submitted.
Student reflected no understanding of his/her work; he/she was unable
to answer any of colleagues and instructor’s questions.
Creativity& enrichment
Student had an outstanding addition in all
aspects of his/her project.
Student had an outstanding addition in some aspects of his/her project.
Student had an outstanding addition in very
few aspects of his/her project.
Student had an outstanding addition in no
aspects of his/her project.
10%
____
____
This rubric is out of 100, percentage orientation.
To make the mark out of 30 (Student’s Mark/10*3)
Total ----> ____
7