[1] A re-design of course outline developed by Mrs. V. July
[2] MTH 112 related material may be found at https://prejudice.tripod.com/lectures/mth112.htm, later on in the course.
Mth
112: Analytical Geometry[1]
Credit
Value: 4 Credits = 8 hrs lectures, 2 hrs tutorials
Duration:
7 weeks (summer 2000/2001)
Lecturer:
Ms. Anesa Hosein - (email: anesa_h@yahoo.com)[2]
Room:
E 18 (Upstairs Physics building)
After
completing this course you should be able to do the following:
·
Find
the locus of any equation under the given description and derive the equation
of the given locus
·
Set
up an equation of a straight line in any form; find the coordinates of the
point of intersection of two given lines
·
Verify
the type of the Conic section from the given general equation of a Cone
·
Distinguish
between orthogonal, internally, externally touching circles, solve any
applicable problem involving intersecting, touching and orthogonal circles
·
Find
the characteristics of the given parabola, hyperbola, ellipse in standard and
translated axes
·
Sketch
curves in polar coordinates
·
Find
the equations of Conic Sections in polar coordinates and recover the type of
conic section from the given equation in polar coordinates
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Units |
Assessment |
Topics and Course Outline |
Notes |
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A. Introduction to Analytical Geometry and Lines |
Wk 1 |
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Introduction. Rectangular Cartesian coordinate
system. Distance between two points. The mid-point of the straight line
joining two given points |
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Quiz
1-2 |
The
locus of an equation. The equation of the Locus of the variable point.
Examples of the loci |
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Gradient
of a straight line. Types of gradients |
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Conditions
for parallel and perpendicular lines. |
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Quiz
3-5 |
The
straight line and its equations |
Wk 2 |
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Points
dividing a line segment in a given ration internally and externally |
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Point
of intersection of two lines |
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Determination
of an acute angle between two lines given in general form |
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Equation
of the line that makes a given angle with the line in general form |
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Quiz
6-10 |
Determination
of the angles of a triangle, given by equation of its sides |
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B. Conic
Sections
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Coordinate
geometry of Conic section. Unified description of Conic Section. General
Equation of Conic Section |
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The
Circle.
Definition, general equation of a circle |
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Equation
of the tangent line to the circle at a given point |
Wk 3 |
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Quiz
11-14 |
Equation
of a circle through three given non-collinear points |
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Equation
of a circle with a given diameter. Length of a tangent from an external point |
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The
common chord of two intersecting circles. The condition that two circles
should intersect. |
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Test#1:
1-17 |
Condition
that two circles should touch externally and internally. Orthogonal circles. |
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Quiz
15-18 |
The
Parabola:
Focus, directrix, vertex and axes of a parabola |
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Graphing
parabolas |
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Equation
of the chord to the parabola at the given point. Equation of the tangent line
to the parabola at the given point. |
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Condition
for the line with the given gradient m to be the tangent to the
given parabola. |
Wk 4 |
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Quiz
19-22 |
Parabola
in translated axes |
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The
Ellipse: Focus, directrix, and eccentricity of an ellipse |
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Equation
of the Ellipse. Graphing ellipses |
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A
second definition of the ellipse |
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Quiz
23-26 |
Equation
of the chord to the ellipse. Equation of the tangent line to the ellipse at
the given point |
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Condition
for the line with the given gradient m to be the tangent to the
ellipse. |
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Test#2:18-28 |
The
Ellipse and translation of axes |
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The
Hyperbola: Focus Directrix and eccentricity of the hyperbola |
Wk 5 |
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Quiz
27-30 |
General
equation of the hyperbola. Graphing hyperbola |
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Asymptotes
of a hyperbola. Rectangular hyperbola. |
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A
second definition of the hyperbola |
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Quiz
30-33 |
Equation
of a chord to the hyperbola. Equation of a tangent line to the hyperbola at a
given point |
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Condition
for the line with given gradient m to be the tangent of the
hyperbola |
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The
hyperbola and translated axes |
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C. Polar Coordinates
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Polar
Coordinates:
The Pole, Radial line. Plotting points in polar coordinates |
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Quiz
34-37 |
Sketching
curves in polar coordinates |
Wk 6 |
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Standard
equations of a conic in polar coordinates |
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Equation
of lines in polar coordinates |
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Equation
of circles in polar coordinates |
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Quiz
38-41 |
Equation
of parabola in polar coordinates |
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Equation
of hyperbola in polar coordinates |
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Cardioid.
N-petal Rose |
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Quiz
42-44 |
Lemniscate.
Spiral |
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Test
#3:29-44 |
Review |
Wk 7 |
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Final Exam Units 1- 44 |
Assessment:
Course work = 40 %, Final Exam= 60 %. Final Exam 2 hrs in the 7th
week.
Coursework:
3 tests (25 %), Quizzes (10 %) and Assignments (5%), Total = 40 %. All tests,
assignments and quizzes are compulsory. Quizzes will be held twice weekly
during the tutorial hours.
References:
|
No. |
Author |
Title |
Publisher, Edition and
Place |
Year |
|
1 |
Anton,
H. |
Calculus
with Analytical Geometry |
4th
Ed. John Wiley & Sons Inc. USA |
1992 |
|
2 |
Barnett,
R.A & Tiengeer, M.R. |
College
Algebra with Trigonometry |
McGraw-Hill,
New York |
1989 |
|
3 |
Bostock,
L. & Chandler, S. |
Mathematics
– The Core Course for A level |
Stanley
Thornes, Cheltenham, U.K. |
1985 |
|
4 |
Foster,
A. & Winters, L.J. |
Algebra
Two and Trigonometry |
Charles
and Merrel Publishing Co., Ohio |
1983 |
|
5 |
Hackworth,
R. & Alwin, R. |
Focus
on Intermediate Algebra |
H&H
Publishing Company, Inc. , USA |
1993 |
|
6 |
Sisan,
C. & Atchinson, W. |
Analytic
Geometry |
Holt,
Rinehart and Winston, 3rd Ed. |
1955 |
|
7 |
Smart,
W. |
Foundation
of Analytical Geometry |
Longmans
Pub. |
1964 |
[1] A re-design of course outline developed by Mrs. V. July
[2] MTH 112 related material may be found at https://prejudice.tripod.com/lectures/mth112.htm, later on in the course.