CIRCLE
(Lesson 6)
Math 14
Plane and Analytic Geometry
OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
Determine the center and radius of the circle
given an equation.
Determine the general and standard form of
equation of th
LESSON ONE: Fundamental Concepts
Problem Set 1
DISTANCE FORMULA
1. Find the distance between the points (4, -2) and (6, 5).
2. By addition of line segments show whether the points A(-3, 0), B(-1, -1) and C(5, -4)
lie on a straight line.
3. The vertices of
ROTATION OF AXIS
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected to be
able to:
transform an equation by rotation of axes.
simplify the equations by rotation of axes.
identify a conic given an equati
ALGEBRAIC CURVES
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is
expected to be able to:
define and describe the properties of
algebraic curves
identify the intercepts of a curve
test the equation of a cur
POLAR CURVES
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
define polar coordinates.
plot points of polar coordinates.
write and sketch the graphs of polar equations.
convert polar t
SPACE COORDINATES AND
SURFACES
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
define space coordinates.
plot points of space coordinates.
write and sketch the graphs of space coord
EXIT EXAM REVIEW - ANALYTIC GEOMETRY
Choose the best answer. Show complete solution. Encircle final answer and write the letter that
match your answer. No solution no points.
1. Determine the y-intercept of the line which passes through (5, 6) and (3, -4)
1.
2.
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PLANE & SOLID ANALYTIC GEOMETRY
LONG QUIZ 1
3rd Quarter sv 2012-2013
Answer the following problems on your separate answer sheet:
TRUE OR FALSE. Write TRUE if the following
assertion is valid, write FALSE o
PLANE and SOLID ANALYTIC GEOMETRY
(MATH 14
LONG gurz #3 '
3rrJl Quarter/20122013
l. COMPREHENSIDN: Classify the following statements as TRUE or FALSE. (2 points
each)
1. For a non-degenerate conic, if the discriminant is equal to 1, the graph is a
parab
Mattias Institute attenuate
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_ Math14 Quiz #2
3' Quarter AY 29122013
I. , True or False. (2 points each)
. a. A conic with eccentricity less than one is ahyperbola.
. The point (1,1) may be an end of iatus rectum of a parabol
CONIC SECTIONS
Examples:
1. Water spouts from a horizontal pipe 40
feet above the ground. Twenty feet below
the line of the pipe, the water stream is at
a horizontal distance of 16 feet from the
vertical line through the end of the pipe.
How far from the
HYPERBOLA
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected to
be able to:
give the properties of hyperbola.
write the standard and general equation of a
hyperbola.
sketch the graph of hyperbola accur
ELLIPSE
thesetofallthepathsofapointwhichm ovesintheplanesothatthesumofitsdistancesfrom twofixedpointint
planeisconstant.Theconstantsumisdenotedby2a
ECCENTRI CI TY
m easurethedegreeofflatnessofanellipse
theeccentricityofanellipseshouldbelessthan1.
FOCALCH
DIVISION OF LINE
SEGMENT
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
Determine the coordinates of a point of
division of a line segment.
- Use this concept to solve common applica
Fundamental Concepts
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected to be
able to:
use the Cartesian Coordinate System efficiently and
effectively as a tool in the study of Analytic Geometry.
dete
INCLINATION AND SLOPE
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
define and determine the angle of inclination
and slope of a single line, as well as of, parallel
lines, perpendi
CIRCLES
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
Determine the center and radius of the circle
given an equation.
Determine the general and standard form of
equation of the ci
,
.
Definitions of Terms
algebraic curve - a curve whose equation can be written in the form f( x, y ) = 0 , where f is a
polynomial in x and y
Intercepts
- are points where the curve crosses the coordinate axes. There are two types of
intercepts: x-inter
ELLIPSE
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
define ellipse
give the different properties of an ellipse with
center at ( 0,0)
identify the coordinates of the different pr
PARABOLA
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is
expected to be able to:
define conic section
identify the different conic section
describe parabola
convert general form to standard form of
equatio
LINES AND
FIRST DEGREE
EQUATIONS
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
Define and determine the general equation of a
line
Define and determine the different standard
equat
PARAMETRIC EQUATIONS
Math 14
Plane and Solid Analytic
Geometry
OBJECTIVES:
At the end of the lesson, the student is expected
to be able to:
define parametric equation.
sketch the graphs of parametric equations by point
plotting.
find the equation by el
TRANSLATION OF AXIS
Math 14
Plane and Solid Analytic
Geometry
Translation of
Axes
OBJECTIVES:
At the end of the lesson, the student is expected to be
able to:
translate coordinate axes.
find new coordinates after translation.
find new equation if the orig
DIVISION OF A LINE
SEGMENT
Internal Point of Division
P2 x2 , y2
P1 P
r
P1 P2
P x , y
P1 x1 , y1
M x , y1
N x2 , y1
External Point of Division
P x , y
P1 P
r
P1 P2
P2 x2 , y2
P1 x1 , y1
M x , y1
N x2 , y1
note : For external point, P is always f
ANGLE BETWEEN
TWO
INTERSECTING
LINES
ANGLE BETWEEN TWO
The angle INTERSECTING LINES L1 and L2
between two intersecting lines
is the least or acute counterclockwise angle.
L2
m2 m1
tan
1 m1m2
L1
Where: m1 = slope of the initial side
m2 = slope of the term
ANALYTIC GEOMETRY
SPECIFIC OBJECTIVES:
At the end of the lesson, the student is expected to be
able to:
Familiarize with the use of Cartesian Coordinate
System.
Determine the distance between two points.
Define and determine the angle of inclinations a