10.6 graphing and classifying conics
- 2. Translated Parabolas Standard form – (h, k) is the vertex Horizontal Axis Vertical Axis Writing an Equation: Make a sketch to determine direction. Plug in h and k (from vertex). Distance between vertex and focus is p. Opens up or right: p is positive Opens down or left: p is negative
- 3. Example: Write an equation of the parabola with vertex (-2, 1) and focus (-3, 1).
- 4. Translated Circles Standard form: Center is (h, k). Graphing: Plot the center. Plot 4 points r units away. Draw the circle.
- 6. Translated Ellipses Standard form – (h, k) is the center Horizontal Major Axis Vertical Major Axis Writing an Equation: Make a sketch. Find center – halfway between vertices. a is distance from vertex to center. c is from focus to center.
- 7. Example: Write an equation of the ellipse with foci at (3, 5) and (3, -1) and vertices at (3, 6) and (3, -2).
- 8. Translated Hyperbolas Standard form – (h, k) is the center Horizontal Axis Vertical Axis Graphing: Plot the center (h, k). Then graph as before.
- 10. Classifying Conics Any conic can be written in the form: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 The discriminant, B2 – 4AC, is used to classify. Discriminantis: Type of Conic < 0, B = 0 and A = C Circle < 0, and either B ≠ 0 or A ≠ C Ellipse = 0 Parabola > 0 Hyperbola
- 11. To Graph: Classify first using discriminant. Write in standard form. Use Complete The Square Graph as before.
- 12. Example: Classify and graph the conic given by 2x2 + y2 – 4x – 4 = 0
- 13. Example: Classify and graph the conic given by 4x2 – 9y2 + 32x – 144y – 548 = 0
- 14. Your Turn! Classify and graph the conic given by 2x2 + y2 + 8y + 6 = 0