About This Chapter
Analytical Geometry in Precalculus - Chapter Summary
This chapter can help you refresh your knowledge of analytical geometry. Watch as our professional instructors explain linear equations on the x-y axis and standard equations for circles and ellipses. Then discover how to graph these geometric forms as the instructors walk you through example problems. If at any time you become confused on any of these topics, ask our instructors for clarification so that you can master the material on:
- The equation for straight lines on the x-y axis
- Characteristics of standard parabolas
- Area and circumference of a circle
- Formula for a circle
- Finding a circle's center and radius on a graph
- How to use the standard equation for ellipses
- The characteristics of hyperbolas
Watch these brief videos then take quizzes that will help you reinforce the material discussed and point out areas you may still want to review. Print out the worksheets to review these concepts on your own. When reviewing areas of weakness, use video tags found on the timeline of each video to go to key parts of the lesson videos. Transcripts are available that present the same information covered in the videos but in an alternative written format.
1. Identifying the Line of Symmetry: Definition & Examples
The line of symmetry, or the invisible line in the center of a shape or line, can be identified algebraically or graphically. Discover more about the line of symmetry, including how to find it using a graph, using a formula, and some examples of them.
2. The Parabola: Definition & Graphing
In mathematics, a parabola is a u-shaped figure that looks similar to an arc. Learn about the definition, standard form equation, and how to graph a horizontal/vertical parabola.
3. Circles: Area and Circumference
Like all geometric shapes, circles take up space and a formula is required to calculate the area. Learn about the area and circumference of circles, explore the formula to calculate a circle's area, and review examples that use the diameter and others that use the circumference to find the area of a circle.
4. Graphing Circles: Identifying the Formula, Center and Radius
Graphing a circle requires knowing the center, radius, and circle formula. Changing the exponents in the formula changes the size and location on the graph. Learn how to to correctly graph a circle by identifying the formula, center, and radius.
5. Defining and Graphing Ellipses in Algebra
An ellipse is a circle that has been stretched, with the horizontal path from the radius shorter than the vertical. Learn how to define the ellipse, and how the equation is used in the graphing of ellipses in algebra.
6. The Hyperbola: Definition, Vertices, Foci & Graphing
The standard equation of a hyperbola can be used to identify its vertices and foci for graphing. Learn the definition and standard equation of a hyperbola, understand how to identify its vertices and foci, and practice graphing with an example.
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Other chapters within the GRE Math: Study Guide & Test Prep course
- Functions in Precalculus
- Polynomial Equations in Precalculus
- Logarithms & Trigonometry
- Limits of Sequences & Functions
- Calculating Derivatives
- Curve Sketching in Precalculus
- Differentiable Functions & Min-Max Problems
- Indefinite Integrals in Calculus
- Definite Integrals in Calculus
- Additional Topics in Calculus
- L'Hopital's Rule, Integrals & Series in Calculus
- Analytic Geometry in 3-Dimensions
- Partial Derivatives
- Calculus: Min/Max & Integrals
- Algebra: Differential Equations
- Algebra: Matrices & Vectors
- Algebra: Determinants & Transformations
- Algebra: Number Theory & Abstract Algebra
- Additional Topics: Sets
- Additional Topics: Unions & Intersections
- Additional Topics: Graphing & Probability
- Additional Topics: Standard Deviation
- Additional Topics: Topology & Complex Variables
- Additional Topics: Trigonometry
- Additional Topics: Theorems, Analysis & Optimizing
- GRE Math Flashcards