Analytic Geometry Lecture 11

Lesson Objectives - the students should be able to:

• Classify equations of the conic sections into parabola, ellipse, and hyperbola
• Graph the parabola in different standard positions with vertex at the origin.
• Graph the parabola with vertex at (h, k)
• Solve problems regarding parabola, finding the vertex, eccentricity and length of the latus rectum.
• Know the different real life applications of parabola.

LESSON OUTLINE:

• Definition
• Parabola with vertex at the origin
• Parabola opening to the right
• Parabola opening to the left
• Parabola opening upward
• Parabola opening downward
• Seatwork
• Homework
• PARABOLA WITH VERTEX AT (h,k)
• Case I : Axis is parallel to the x-axis and the parabola opens to the right,
• Case II : Axis is parallel to the x-axis and the parabola opens to the left,
• Case III : Axis is parallel to the y-axis and the parabola opens upward,
• Case IV : Axis is parallel to the y-axis and the parabola opens downward,
• Examples
• Summaries
• Seatwork
• Homework

Analytic Geometry Lecture 11

Analytic Geometry Course Outline

Following is the list of topics we will discuss in this course:

I. Plane Analytic Geometry

LESSON 1: Introduction to Geometry, Directed Line Segments, The Cartesian Plane, Distance Formula

LESSON 2: Midpoint of a Line, Point-of-Division Formulas

LESSON 3: Slope of a Line in term of Angle inclination, Slope of a line in terms of Coordinate

LESSON 4: Slope of Perpendicular lines, Slope of Parallel Lines, Angle formed between two lines

LESSON 5: Finding the equation of a line using Two-point Form and Intercept Form

LESSON 6: Finding the equation of a line using Slope-Point Form and Slope-Intercept Form

LESSON 7: Finding the other forms of equation of a lines and Finding the Family of Lines

LESSON 8: Changing from General Form to Standard Equation of a line and Finding distance from line to a point

LESSON 9: Standard form of the equation of the circle, Equation of circles with center at origin, General form of the equation of a circle

LESSON 10: Determine Circles by Geometric Conditions

LESSON 11: Conic Sections: Parabola

LESSON 12: Conic Sections: Ellipse

LESSON 13: Conic Sections: Hyperbola

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