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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

  1.  

 

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

  1.  

Quiz 1-2

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

  1.  

 

Gradient of a straight line. Types of gradients

  1.  

 

Conditions for parallel and perpendicular lines.

  1.  

Quiz 3-5

The straight line and its equations

Wk 2

 

  1.  

 

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

  1.  

 

Point of intersection of two lines

  1.  

 

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

  1.  

 

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

  1.  

Quiz 6-10

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

 

 

 

 

 

B. Conic Sections

  1.  

 

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

  1.  

 

The Circle. Definition, general equation of a circle

  1.  

 

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

Wk 3

  1.  

Quiz 11-14

Equation of a circle through three given non-collinear points

  1.  

 

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

  1.  

 

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

  1.  

Test#1: 1-17

Condition that two circles should touch externally and internally. Orthogonal circles.

  1.  

Quiz 15-18

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

  1.  

 

Graphing parabolas

  1.  

 

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

  1.  

 

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

Wk 4

  1.  

Quiz 19-22

Parabola in translated axes

  1.  

 

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

  1.  

 

Equation of the Ellipse. Graphing ellipses

  1.  

 

A second definition of the ellipse

  1.  

Quiz 23-26

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

  1.  

 

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

  1.  

Test#2:18-28

The Ellipse and translation of axes

  1.  

 

The Hyperbola: Focus Directrix and eccentricity of the hyperbola

Wk 5

  1.  

Quiz 27-30

General equation of the hyperbola. Graphing hyperbola

  1.  

 

Asymptotes of a hyperbola. Rectangular hyperbola.

  1.  

 

A second definition of the hyperbola

  1.  

Quiz 30-33

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

  1.  

 

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

  1.  

 

The hyperbola and translated axes

 

 

 

 

 

C. Polar Coordinates

  1.  

 

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

  1.  

Quiz 34-37

Sketching curves in polar coordinates

Wk 6

  1.  

 

Standard equations of a conic in polar coordinates

  1.  

 

Equation of lines in polar coordinates

  1.  

 

Equation of circles in polar coordinates

  1.  

Quiz 38-41

Equation of parabola in polar coordinates

  1.  

 

Equation of hyperbola in polar coordinates

  1.  

 

Cardioid. N-petal Rose

  1.  

Quiz 42-44

Lemniscate. Spiral

  1.  

Test #3:29-44

Review

Wk 7

  1.  

 

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

 

  Back to Mth 112 page


[1] A re-design 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.