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Conic section

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Algebra and Trigonometry

Definition

A conic section is a curve obtained by intersecting a cone with a plane. The four types are circles, ellipses, parabolas, and hyperbolas.

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5 Must Know Facts For Your Next Test

  1. The general equation of a conic section in rotated axes can be written as $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$.
  2. Rotation of axes can eliminate the $Bxy$ term, simplifying the conic section's equation.
  3. To rotate the axes to eliminate the $Bxy$ term, use the angle $\theta$ where $\tan(2\theta) = \frac{B}{A - C}$.
  4. A hyperbola is formed when the plane intersects both nappes of the cone.
  5. In analytic geometry, completing the square is often used to rewrite conic sections in their standard forms.

Review Questions

  • What happens to the $Bxy$ term when you rotate the axes correctly?
  • How do you determine the angle of rotation for eliminating the $Bxy$ term in a conic section's equation?
  • What are the four types of conic sections?
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