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Conic Sections

Conic Sections. The conic sections are curves that can be constructed from the intersection of a plane with a cone. All of these curves can be written in the form: Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0. A and C same sign A ≠ C. A = C.

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Conic Sections

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  1. Conic Sections The conic sections are curves that can be constructed from the intersection of a plane with a cone

  2. All of these curves can be written in the form: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 A and C same sign A ≠ C A = C

  3. All of these curves can be written in the form: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 A = 0 or C = 0 (only one variable squared) A and C diff. sign

  4. Ex. Classify the conic • 6x2 + 6y2 – 162 = 0 • x2 – 8y = 0 • 4x2 + 2y2 – 8 = 0 • 4y2 – x2 + 4 = 0 • x2 + y2 + 6y – 27 = 0 • x2 – y2 + 8x – 16 = 0

  5. Pract. Classify the conic • 3x2 + 4y2 + 8y – 8 = 0 • x2 + y2 – 8y + 11 = 0 • 9x2 + 25y2 – 54x – 50y – 119 = 0 • 25x2 – 9y2 – 18y + 219 = 0 • x2 + 8x + y + 23 = 0

  6. Circles General form is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 where A = C Standard form: Center: Radius:

  7. Ex. Write the equation of the circle. • Find the center • Find the radius • Simplify

  8. 1) Write the equation of the circle.

  9. 2) Write the equation of the circle with center at (-3,10) and a radius of .

  10. 1) Graph the circle x2 + (y – 3)2 = 9

  11. If necessary, put in standard form by completing the square. 2) Graph the circle x2 + y2 = 14x – 24

  12. 3) Graph the circle x2 + y2 – 4x + 6y + 4 = 0

  13. Every homework assignment this chapter will include review from previous chapters  The test will include review problems

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