1 / 7

8.6 Conic Sections

8.6 Conic Sections. Write equations of conic sections in standard form Identify conic sections from their equations. 8.6 Conic Sections. The equation of any conic section can be written in the general quadratic equation: Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 where A, B, and C ≠ 0

Download Presentation

8.6 Conic Sections

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 8.6 Conic Sections Write equations of conic sections in standard form Identify conic sections from their equations

  2. 8.6 Conic Sections The equation of any conic section can be written in the general quadratic equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 where A, B, and C ≠ 0 If you are given an equation in this general form, you can complete the square to write the equation in one of the standard forms you have already learned.

  3. Standard Forms (you already know )

  4. Identifying Conic Sections

  5. Example One: Write each equation in standard form. Then state whether the graph of the equation is a parabola, circle, ellipse, and hyperbola. y = x2 + 4x + 1 x2 + y2 = 4x + 2 y2 – 2x2 – 16 = 0 x2 + 4y2 + 2x – 24y + 33 = 0

  6. Example Two: Without writing the equation in standard form, state whether the graph of each equation is a parabola, circle, ellipse, and hyperbola. x2 + 2y2 + 6x – 20y + 53 = 0 x2 + y2 – 4x – 14y + 29 = 0 3y2 + x – 24y + 46 = 0 6x2 – 5y2 + 24x + 20y – 56 = 0

  7. Your Turn: Without writing the equation in standard form, state whether the graph of each equation is a parabola, circle, ellipse, and hyperbola. x2 + y2 – 6x + 4y + 3 = 0 6x2 – 60x – y + 161 = 0 x2 – 4y2 – 16x + 24y – 36 = 0 x2 + 2y2 + 8x + 4y + 2 = 0

More Related