Math 2 : 0 Analytic Geometry

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BS002: Mathematics 2 Analytic Geometry

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Plane Geometry

Space Geometry

Algebra Series

Complex Numbers

Linear Algebra

Assessment

Participation . 10%

Quizzes .... 20%

Midterm .. 20%

Final Exam .. 50%

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Math 2 : 0 Analytic Geometry

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Textbooks

Smith and Minton

Calculus

4th ed., McGraw Hill 2012

Duffy

Advanced Engineering Mathematics,

CRC Press 1998

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Learning Material https://sites.google.com/site/sahaggag

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Syllabus Slides Problem sheets Bonus Questions Announcements Grades

Math 2 : 0 Analytic Geometry

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Plane Geometry

0 Review of Analytic Geometry

1 Conic Sections

2 Parametric Equations

3 Polar Coordinates

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0 Review of Analytic Geometry

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Reading Stewart

Review of Analytic Geometry

Problems Sheet 0

Math 2 : 0 Analytic Geometry

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Analytic Geometry

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Point ?

origin

x-coordinate

Rectangular (Cartesian) Coordinates

x-axis y-axis

y-coordinate

in the plane

The Cartesian Plane

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4 quadrants

Math 2 : 0 Analytic Geometry

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Example 1

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x = 4 ?

y = 2 ?

equation? line

Example 2

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x 0 ? |y| < 1 ?

1 < y < 1

inequality region

Math 2 : 0 Analytic Geometry

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Distance Between 2 Points

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1 2P P 2 2

2 1 2 1x x y y

Lines

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m y

x

2 1

2 1

y y

x x

slope ?

Parallel Lines ?

Math 2 : 0 Analytic Geometry

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Example 3

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Perpendicular Lines ?

Equations of a Line

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( , ),1 1P x y m

1

1

y ym

x x

Point-Slope

( , ), ( , )1 1 1 2 2 2P x y P x y

1 2 1

1 2 1

y y y y

x x x x

Two Points

,m by m x b

Slope-Intercept

Math 2 : 0 Analytic Geometry

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Equation of a Curve

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is an equation satisfied by x and y of the points on the curve

The circle is the set of all points that are at a fixed distance (called the radius) from a fixed point (called the center).

The Circle ?

The Line ? 0a x by c

Definition Equation ?

Simple Equation of a Circle

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Center Radius

at origin r

equation ?

2 2 2x y r

?

?

22 2

2

rx y

r

inside

outside

r = 1 unit circle

Math 2 : 0 Analytic Geometry

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General Circles

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general ?

Center Radius

(h , k) r

equation ?

2 2 2x h y k r

?

?

22 2

2

rx h y k

r

inside

outside

More Examples

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See Stewarts Review of Analytic Geometry Examples 1 6

Problems Sheet 0 Problems from Stewarts Exercises