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

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

5. 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 Vertices: ( 1+2 2 , 0)
c2 = 8 – 4 (1- 2 2 , 0)
c2 = 4
c=2 Foci: (3, 0), (-1, 0)

6. 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)

7. (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)