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
Units 
Assessment 
Topics and Course Outline 
Notes 






A. Introduction to Analytical Geometry and Lines 
Wk 1 


Introduction. Rectangular Cartesian coordinate
system. Distance between two points. The midpoint of the straight line
joining two given points 


Quiz
12 
The
locus of an equation. The equation of the Locus of the variable point.
Examples of the loci 



Gradient
of a straight line. Types of gradients 



Conditions
for parallel and perpendicular lines. 


Quiz
35 
The
straight line and its equations 
Wk 2 


Points
dividing a line segment in a given ration internally and externally 



Point
of intersection of two lines 



Determination
of an acute angle between two lines given in general form 



Equation
of the line that makes a given angle with the line in general form 


Quiz
610 
Determination
of the angles of a triangle, given by equation of its sides 







B. Conic
Sections




Coordinate
geometry of Conic section. Unified description of Conic Section. General
Equation of Conic Section 



The
Circle.
Definition, general equation of a circle 



Equation
of the tangent line to the circle at a given point 
Wk 3 

Quiz
1114 
Equation
of a circle through three given noncollinear points 



Equation
of a circle with a given diameter. Length of a tangent from an external point 



The
common chord of two intersecting circles. The condition that two circles
should intersect. 


Test#1:
117 
Condition
that two circles should touch externally and internally. Orthogonal circles. 


Quiz
1518 
The
Parabola:
Focus, directrix, vertex and axes of a parabola 



Graphing
parabolas 



Equation
of the chord to the parabola at the given point. Equation of the tangent line
to the parabola at the given point. 



Condition
for the line with the given gradient m to be the tangent to the
given parabola. 
Wk 4 

Quiz
1922 
Parabola
in translated axes 



The
Ellipse: Focus, directrix, and eccentricity of an ellipse 



Equation
of the Ellipse. Graphing ellipses 



A
second definition of the ellipse 


Quiz
2326 
Equation
of the chord to the ellipse. Equation of the tangent line to the ellipse at
the given point 



Condition
for the line with the given gradient m to be the tangent to the
ellipse. 


Test#2:1828 
The
Ellipse and translation of axes 



The
Hyperbola: Focus Directrix and eccentricity of the hyperbola 
Wk 5 

Quiz
2730 
General
equation of the hyperbola. Graphing hyperbola 



Asymptotes
of a hyperbola. Rectangular hyperbola. 



A
second definition of the hyperbola 


Quiz
3033 
Equation
of a chord to the hyperbola. Equation of a tangent line to the hyperbola at a
given point 



Condition
for the line with given gradient m to be the tangent of the
hyperbola 



The
hyperbola and translated axes 







C. Polar Coordinates




Polar
Coordinates:
The Pole, Radial line. Plotting points in polar coordinates 


Quiz
3437 
Sketching
curves in polar coordinates 
Wk 6 


Standard
equations of a conic in polar coordinates 



Equation
of lines in polar coordinates 



Equation
of circles in polar coordinates 


Quiz
3841 
Equation
of parabola in polar coordinates 



Equation
of hyperbola in polar coordinates 



Cardioid.
Npetal Rose 


Quiz
4244 
Lemniscate.
Spiral 


Test
#3:2944 
Review 
Wk 7 


Final Exam Units 1 44 
Assessment:
Course work = 40 %, Final Exam= 60 %. Final Exam 2 hrs in the 7^{th}
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 
4^{th}
Ed. John Wiley & Sons Inc. USA 
1992 
2 
Barnett,
R.A & Tiengeer, M.R. 
College
Algebra with Trigonometry 
McGrawHill,
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, 3^{rd} Ed. 
1955 
7 
Smart,
W. 
Foundation
of Analytical Geometry 
Longmans
Pub. 
1964 
[1] A redesign of course outline developed by Mrs. V. July
[2] MTH 112 related material may be found at http://prejudice.tripod.com/lectures/mth112.htm, later on in the course.