1. More Conic Sections

2. Objective Given a translation, I can graph an equation for a conic section.

3. Ellipses (x-h) 2 + (y-k) 2 = 1 a 2 b 2 where a > b Center: (h, k) Major axis: y = k (horizontal) Minor axis: x = h (vertical) Vertices: (h-a, k), (h+a, k) Co-vertices: (h, y+b), (h, y-b) Foci: (h+c, k), (h–c, k) where c 2 = a 2 – b 2

4. Ellipses (y-k) 2 + (x-h) 2 = 1 a 2 b 2 where a > b Center: (h, k) Major axis: x = h (vertical) Minor axis: y=k (horizontal) Vertices: (h, y+a), (h, y-a) Co-vertices: (h-b, k), (h+b, k) Foci: (h, k+c), (h, k–c) where c 2 = a 2 – b 2

5. Graphing Ellipses Identify Center Major axis Minor axis Vertices Co-vertices Foci

6. Graphing Ellipses Identify Center Major axis Minor axis Vertices Co-vertices Foci

7. Parabolas (x-h) 2 = 4p(y-k) Vertex: (h, k) Axis of symmetry: x = h Focus: (h, k + p) Directrix: y = k – p Length of Latus Rectum: |4p| If p > 0, opens upward If p < 0, opens downward

8. Parabolas (y-k) 2 = 4p(x-h) Vertex: (h, k) Axis of symmetry: y = k Focus: (h = p, k) Directrix: x = h – p Length of Latus Rectum: |4p| If p > 0, opens right If p < 0, opens left

9. Graphing Parabolas Identify Vertex Axis of symmetry Focus Directrix Length of Latus Rectum

10. Graphing Parabolas Identify Vertex Axis of symmetry Focus Directrix Length of Latus Rectum

11. Hyperbolas

13. (x-h) 2 – (y-k) 2 = r 2 a 2 b 2 Center: (h, k) Transverse axis: y = k (horizontal) Conjugate axis: x = h (vertical) Vertices: (h-a, k), (h+a, k) Foci: (h-c, k), (h+c, k) where c 2 = a 2 + b 2 Asymptotes: y = k ± (b/a)(x – h) Width of inside rectangle: 2a Height of inside rectangle: 2b Corners of rectangle: (h-a, k+b), (h+a, k+b), (h-a, k-b), (h+a, k-b)

14. Hyperbolas (y-k) 2 – (x-h) 2 = r 2 a 2 b 2 Center: (h, k) Transverse axis: x = h (horizontal) Conjugate axis: y = k (vertical) Vertices: (h, k-a), (h, k+a) Foci: (h, k-c), (h, k+c) where c 2 = a 2 + b 2 Asymptotes: y = k ± (a/b)(x – h) Width of inside rectangle: 2b Height of inside rectangle: 2a Corners of rectangle: (h-b, k+a), (h+b, k+a), (h-b, k-a), (h+b, k-a)

15. Graphing Hyperbolas Identify Center Transverse axis Conjugate axis Vertices Foci Asymptotes Corners of rectangle

16. Graphing Hyperbolas Identify Center Transverse axis Conjugate axis Vertices Foci Asymptotes Corners of rectangle