Table of contents
- 0. Fundamental Concepts of Algebra3h 29m
- 1. Equations and Inequalities3h 27m
- 2. Graphs1h 43m
- 3. Functions & Graphs2h 17m
- 4. Polynomial Functions1h 54m
- 5. Rational Functions1h 23m
- 6. Exponential and Logarithmic Functions2h 28m
- 7. Measuring Angles40m
- 8. Trigonometric Functions on Right Triangles2h 5m
- 9. Unit Circle1h 19m
- 10. Graphing Trigonometric Functions1h 19m
- 11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
- 12. Trigonometric Identities 2h 34m
- 13. Non-Right Triangles1h 38m
- 14. Vectors2h 25m
- 15. Polar Equations2h 5m
- 16. Parametric Equations1h 6m
- 17. Graphing Complex Numbers1h 7m
- 18. Systems of Equations and Matrices3h 6m
- 19. Conic Sections2h 36m
- 20. Sequences, Series & Induction1h 15m
- 21. Combinatorics and Probability1h 45m
- 22. Limits & Continuity1h 49m
- 23. Intro to Derivatives & Area Under the Curve2h 9m
19. Conic Sections
Introduction to Conic Sections
Struggling with Precalculus?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
How can you slice a vertically oriented 3D cone with a 2D plane to get a circle?
A
Slice the cone with a horizontal plane.
B
Slice the cone with a slightly tilted plane.
C
Slice the cone with a heavily tilted plane.
D
Slice the cone with a vertical plane.

1
Understand the geometry of a cone: A cone is a three-dimensional shape with a circular base and a single vertex. When slicing a cone, the orientation of the plane relative to the cone determines the shape of the cross-section.
Identify the goal: To obtain a circle as the cross-section, the plane must intersect the cone in such a way that the intersection is a perfect circle.
Consider the orientation of the plane: A horizontal plane, which is parallel to the base of the cone, will intersect the cone in a circular cross-section. This is because the plane cuts through the cone at a constant distance from the vertex, maintaining the circular shape.
Explore other orientations: A slightly tilted plane can also produce an ellipse, which is a stretched circle. However, for a perfect circle, the plane must be horizontal.
Visualize the intersection: Imagine slicing through the cone horizontally. The plane will cut through the cone parallel to its base, resulting in a circular cross-section. This is the only orientation that guarantees a perfect circle.
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