Conic Sections Basics
A free College Algebra lesson from the “Relating Algebra and Geometry” unit, with a worked example and practice problems including step-by-step solutions.
Conic sections are curves created by slicing cones. In College Algebra, the main goal is recognizing equation patterns and interpreting basic features.
What you'll learn
- Recognize circles, parabolas, ellipses, and hyperbolas
- Connect equations to shapes
- Interpret basic conic features
Worked example
Problem. Which conic is represented by (x - 1)^2 + (y + 2)^2 = 16?
- Both x and y are squared.
- The squared terms have the same coefficient.
- This is a circle with radius 4.
Answer: circle
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. An equation with only x squared, such as y = x^2 + 3, is a...
Choices: Parabola · Circle · Ellipse · Line
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- One squared variable points to a parabola.
Answer: Parabola
2. x^2 + y^2 = 25 represents a...
Choices: Circle · Line · Hyperbola · Cubic
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- Equal squared terms.
Answer: Circle
3. x^2 - y^2 = 9 is a basic pattern for a...
Choices: Hyperbola · Circle · Line · Absolute value graph
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- A difference of squared terms suggests a hyperbola.
Answer: Hyperbola
4. For x^2 + y^2 = 36, what is the radius?
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- The radius squared is 36.
Answer: 6
5. The graph of y = x^2 opens...
Choices: Up · Down · Left · Right
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- The leading coefficient is positive.
Answer: Up
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