2. (y – 4)2 = 8(x – 1) 8(x – 1) = (y – 4)2 8x – 8 = (y – 4)2 8x = (y – 4)2 + 8 x = (y – 4)2 + 1 Parabola Opens right Vertex: (1, 4) Line of symmetry: y = 4 Focus: (3, 4) Directrix: x = -1 Length of latus rectum: 8

3. x2 + y2 + 6y + 13 = 40 x2 + y2 + 6y + 9 = 27 + 9 x2 + (y + 3)2 = 36 Circle Center: (0, -3) Radius: 6

4. x2 + 2y2 = 2x + 7 x2 – 2x + 1 + 2y2 =7 + 1 (x – 1)2 + 2y2 = 8 8 8 8 (x – 1)2 + y2 = 1 8 4 ellipse Center: (1, 0) a = 2 2 b = 2 c2 = 8 – 4 c2 = 4 c = 2 Vertices: ( 1+2 2 , 0) (1- 2 2 , 0) Foci: (3, 0), (-1, 0)

5. y2 – 4x2 – 4y – 8x - 16 = 0 y2 – 4y + 4 – 4(x2 + 2x + 1) = 16 + 4 - 4 (y – 2)2 - 4(x + 1)2 = 16 16 16 16 (y – 2)2 - (x + 1)2 = 1 16 4 Hyperbola Center: (-1, 2)

6. (y – 2)2 - (x + 1)2 = 1 16 4 Center: (-1, 2) a = 4 vertices (-1,3) (-1,1) b = 2 Asymptotes: y = 2x + 4 y = -2x c2 = 16 + 4 c2 = 20 c = 20 Foci: (-1, 2+ 20) (-1, 2- 20)