Honors Algebra II
Chapter 8: Review
1.
Find the distance between the two points. Then find the midpoint of the line segment joining the two points. a.
  
2, 3
 b.
    c.
     
2.
The vertices of a triangle are given. Classify the triangle as scalene, isosoceles , or equilateral.
a.
      b.
     

3.
Write an equation for the perpendicular bisector of the line segment joining the two points. a.
      b.
    c.
  
3, 6

4.
An architect is in charge of building a new governmental building. The center of the lobby is to have a circular dome as part of the ceiling. Three points on the edge of the dome are
 
,
 
3, 2

, and
 
where each unit represents one foot. What is the diameter of the dome (in feet)?

5.
Graph the equation. Identify the focus and directrix of the parabola. a.
x
2 
4 y b.
y
2  
8 x c.
x
2 
12 y

0

6.
Write the standard form of the equation of the parabola with the given focus or directrix and vertex at the origin,
 
. a.
Focus:
  b.
Directrix: x
 
6 c.
Focus:
 
2, 0
 d.
Directrix: y
 
1
4

7.
Graph the equation. Identify the radius of the circle. a.
x
2  y
2 
25 b.
x
2  y
2 
18 c.
3 x
2 
3 y
2 
243

8.
Write the standard form of the equation of the circle with the given radius and whose center is the origin. a.
Radius: 6 b.
Radius: 13
9.
Write the standard from of the equation of the circle that passes through the given point and whose center is the origin,
 
. a.

3, 2


b.

1, 5

10.
Write an equation of the line tangent to the given circle at the given point. a.
x
2  y
2  b.
x
2  y
2 
52;
 
4, 6

11.
A radio station has a broadcast radius of 40 miles. Your house is located 32 miles west and 21 miles south of the radio station. Is house within the broadcast range?
12.
Graph the equation. Identify the vertices, co-vertices, and foci of the ellipse. a.
x
2
 y
2
16 25

1

b.
9 x
2 
4 y
2 
36 c.
4 x
2 
5 y
2 
40
13.
Write an equation of the ellipse with the given characteristics and center at
 
. a.
Vertex:
 
Co-vertex:
 

b.
Vertex:

0, 6

Focus:
  c.
Co-vertex:
Focus:
 

0, 2 5

14.
Graph the equation. Identify the vertices, foci, and asymptotes of the hyperbola. a.
x 2
 y
9 4
2

1 b.
25 y
2 
16 x
2 
400

c.
2 x
2 
10 y
2 
40
15.
Write an equation with the given foci and vertices whose center is at the origin,
 
. a.
Foci:
   
Vertices:
    b.
Foci:
   
6, 0

Vertices:
   
4,0

16.
Graph the equation. Identify the type of conic and then the important characteristics of each corresponding graph. a.
 x

4

2 
4
 y

2


b.
 y

3

2 
8
 x

4
 c.
 x

3
  y

4

2 
48 d.
   y

3

2 
9

e.
 x

16
4
  y

4
2

2

1 f.
 x

36
2
  y

9
5

2

1

g.
 y

2
  x

1

2
16 25

1 h.
 x

4
3
  
2 
1
17.
Write an equation for the conic section. a.
Parabola  Vertex:
 
Focus:
  b.
Ellipse  Foci:
   
2,7

Co-vertices:
  

c.
Circle  Center:

2, 6

Radius: r

4 d.
Hyperbola  Vertices:
(2, 4), (8, 4)
Foci:
    