PRE-CALCULUS ANALYTIC GEOMETRY

About Course

This course offers a comprehensive walkthrough of the Analytic Geometry diagnostic test from the renowned Stewart Calculus textbook. Ideal for students looking to strengthen their foundational understanding before diving into calculus, this course features clear, step-by-step video solutions to each problem on the diagnostic test.

Whether you’re preparing for college-level mathematics, brushing up for an exam, or want to close knowledge gaps in analytic geometry, this course will guide you through essential topics, including:

Coordinate systems and graphing
Lines, slopes, and distances
Conic sections: circles, parabolas, ellipses, and hyperbolas
Basic vector geometry and applications

Understand and apply the coordinate plane to represent points, lines, and curves geometrically.
Write and interpret the equation of a line in different forms (slope-intercept, point-slope, and standard form).
Calculate slopes, distances, and midpoints between two points.
Derive and analyze the equation of a circle, including completing the square to convert from general to standard form.
Identify and work with conic sections—circles, parabolas, ellipses, and hyperbolas—using their standard equations.
Understand symmetry, vertices, foci, and axes associated with conic sections.
Solve geometric problems algebraically, preparing for deeper topics in calculus and vector analysis.
Build confidence through step-by-step video walkthroughs of diagnostic test problems from the Stewart Calculus textbook.

Course Content

EQUATION OF A LINE I
In this lesson, we explore the different ways to express the equation of a line in the coordinate plane. You'll learn how to derive and interpret equations using given points, slopes, and other geometric information.

Finding equation of a line given a point and a slope

03:22
Finding equation of a line given a point and is parallel to the x-axis

05:09
Finding equation of a line given a point and is parallel to the y-axis

01:53
Finding equation of a line given a point and is parallel to another line

05:14

EQUATION OF A LINE II

EQUATION OF A CIRCLE
In this lesson, you’ll learn how to identify and write the equation of a circle in the coordinate plane. We break down the components of the equation and apply them to solve problems similar to those in the Stewart textbook diagnostic test.

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What Will You Learn?

Course Content

EQUATION OF A LINE I
In this lesson, we explore the different ways to express the equation of a line in the coordinate plane. You'll learn how to derive and interpret equations using given points, slopes, and other geometric information.

Finding equation of a line given a point and a slope

Finding equation of a line given a point and is parallel to the x-axis

Finding equation of a line given a point and is parallel to the y-axis

Finding equation of a line given a point and is parallel to another line

EQUATION OF A LINE II

Finding the slope, equation and intercepts of a line given two points

Finding the midpoint and length of a segment given two points

Finding the equation of the perpendicular bisector of two points

EQUATION OF A CIRCLE
In this lesson, you’ll learn how to identify and write the equation of a circle in the coordinate plane. We break down the components of the equation and apply them to solve problems similar to those in the Stewart textbook diagnostic test.

Finding the equation of a circle given the center and a point

Finding the center and radius from the equation of a circle

QUIZ

Earn a certificate

PRE-CALCULUS ALGEBRA

PRE-CALCULUS TRIGONOMETRY

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About Course

What Will You Learn?

Course Content

EQUATION OF A LINE I In this lesson, we explore the different ways to express the equation of a line in the coordinate plane. You'll learn how to derive and interpret equations using given points, slopes, and other geometric information.

Finding equation of a line given a point and a slope

Finding equation of a line given a point and is parallel to the x-axis

Finding equation of a line given a point and is parallel to the y-axis

Finding equation of a line given a point and is parallel to another line

EQUATION OF A LINE II

Finding the slope, equation and intercepts of a line given two points

Finding the midpoint and length of a segment given two points

Finding the equation of the perpendicular bisector of two points

EQUATION OF A CIRCLE In this lesson, you’ll learn how to identify and write the equation of a circle in the coordinate plane. We break down the components of the equation and apply them to solve problems similar to those in the Stewart textbook diagnostic test.

Finding the equation of a circle given the center and a point

Finding the center and radius from the equation of a circle

QUIZ

Earn a certificate

Student Ratings & Reviews

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PRE-CALCULUS ALGEBRA

PRE-CALCULUS TRIGONOMETRY

PRE-CALCULUS FUNCTION

EQUATION OF A LINE I
In this lesson, we explore the different ways to express the equation of a line in the coordinate plane. You'll learn how to derive and interpret equations using given points, slopes, and other geometric information.

EQUATION OF A CIRCLE
In this lesson, you’ll learn how to identify and write the equation of a circle in the coordinate plane. We break down the components of the equation and apply them to solve problems similar to those in the Stewart textbook diagnostic test.