1.

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

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

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

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

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