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Name _____________________________
Date ___________________

Conics
(Answer ID # 0907097)
Find the distance between P and Q and the coordinates of the midpoint between the two points.
1.  
P
(-5  ,  -6)
  and
Q
(
-1
5

6
  ,  -24)
2.  
P
(6  ,  -12)
  and
Q
(-12  ,  -9)

Find the distance between P and Q and the coordinates of the midpoint between the two points.
3.  
P
(
10
  
5
  ,  
6
  
5
)
  and
Q
(
14
  
5
  ,  
9
  
5
)
4.  
P
(
10
  
10
  ,  
8
  
2
)
  and
Q
(
18
  
10
  ,  
14
  
2
)

Point M is the midpoint between the points P and Q. Find the coordinates of the missing point.
5.  
Q
(5  ,  
-5
3

5
)

M
(
8
7

11
  ,  
-3
67

90
)
6.  
P
(-7  ,  -2)

M
(-1  ,  
1

2
)

 

Point M is the midpoint between the points P and Q. Find the coordinates of the missing point.
7.  
P
(
2
  
2
  ,  
10
  
10
)

M
(
13
  
2
2
  ,  
12
  
5
)
8.  
P
(
9
  
6
  ,  
11
  
7
)

M
(
23
  
6
2
  ,  
25
  
7
2
)

The points A and C are the endpoints of a diameter in a circle. Find the point B which is the center of the circle. Also find the circumference and area of the circle.
9.  
A
(-9  ,  1)
  
C
(-13  ,  -7)
10.  
A
(-5  ,  9)
  
C
(-18  ,  -3)

Write the equation of the parabola in standard form.
11.  
y  =  
1

24
x2
12.  
-36x  =  
3

4
y2
13.  
40y  =  x2

 

Find the focus and the directrix of the parabola. The vertex of the parabola is (0,0).
14.  
x + 63  =  
1

44
y2 + 63
15.  
-1

36
x2  =  y
16.  
x  =  
-1

40
y2

Find the focus, vertex, and the directrix of the parabola.
17.  
-4y2  +  8y  +  96x  -  868  =    0  
18.  
y  -  2  =  -
1

44
(x  -  8)2
19.  
x2  -  12x  -  48y  +  276  =    0  

Write the equation for the parabola that has the given characteristics.
20.   focus: (1,0)
directrix: x=-1
21.   vertex: (-9, 4)
focus: (-9, 16)
22.   vertex: (0, 0)
directrix: x=4

 

Write the standard form of the equation of the circle with the given radius and center.
23.  
C (0, 0); r =
1

3
24.  
C (6, 2); r =
12  +  
  
7
25.  
C (0, 0); r =
  
13

Write the standard equation, the center, and the radius for each circle.
26.  
x2 + y2 - 6x + 9  =  
1

36
27.  
x2 + y2 + 6y + 9  =  
1

16

Write the standard form of the equation of the circle with the given center C that passes through the given point Z.
28.  
C (-4, -9); Z (-4, -4)
29.  
C (0, -7); Z (-2, -7)
30.  
C (3, 8); Z (-7, 9)

 

Find the foci, vertices, and co-vertices of each ellipse.
31.  
x2
81
  +  
y2
9
  =    1  
32.  
x2
36
  +  
y2
256
  =    1  
33.  
x2
25
  +  
y2
121
  =    1  

Find the center, foci, vertices, and co-vertices of each ellipse.
34.  
(x   -  5)2
16
  +  
(y   +  2)2
36
  =    1  
35.  
(x   -  1)2
81
  +  
(y   -  7)2
4
  =    1  
36.  
(x   +  7)2
16
  +  
(y   +  6)2
1
  =    1  

Write the standard equation of each ellipse. Find the center, foci, vertices, and co-vertices of each ellipse.
37.  
36x2 + 25y2 - 216x - 100y - 476  =    0  
38.  
3x2  +  
3y2
4
  -    3    =    0  

 

Write the standard equation for the ellipse.
39.   Center (0,0)
Vertex: (0,-6)
Co-Vertex: (3,0)
40.   Center (0,0)
Vertex: (0,9)
Co-Vertex: (-4,0)
41.   Center (0,0)
Vertex: (2,0)
Focus:
(
  
3
  ,  0)

Write the standard equation for the ellipse.
42.  
Foci: 
(3  ,  
  4 -   
 4 
2
)
  and  
(3  ,  
  4 +   
 4 
2
)
co-vertices: (1,4) and (5,4)
43.  
Foci: 
(0  ,  -4)
  and  
(0  ,  4)
co-vertices: (-3,0) and (3,0)

Find the vertices, co-vertices, foci, and asymptotes of the hyperbola.
44.  
x2
169
  -  
y2
121
  =    1  
45.  
y2
36
  -  
x2
9
  =    1  

 

Find the vertices, co-vertices, and foci of the hyperbola.
46.  
(x   +  5)2
9
  -  
(y   +  1)2
9
  =    1  
47.  
(y   +  7)2
16
  -  
(x   -  6)2
81
  =    1  

Write the equation in standard form.  Find the vertices, co-vertices, and foci of the hyperbola.
48.  
y2 - x2 - 4y - 2x - 78  =    0  
49.  
y2
4
  -  
9x2
25
  =    9  

Write the standard equation for the hyperbola with the given characteristics.
50.  
Foci: 
(-10  ,  0)
  and  
(10  ,  0)
co-vertices: (0,-8) and (0,8)

 

Write the standard equation for the hyperbola with the given characteristics.
51.   center: (-3,-3)
Foci: 
(
  -3 -   
 3 
5
  ,  -3)
  and  
(
  -3 +   
 3 
5
  ,  -3)
co-vertices: (-3,-6) and (-3,0)

Classify the conic section.
52.  
(x   +  2)2
49
  -  
(y   +  3)2
64
  =    1  
53.  
x  =  
-1

16
y2

Classify the conic section.  Write the standard equation of the conic section.
54.  
9x2 - 4y2 - 54x - 8y - 247  =    0  
55.  
x + 44  =  
-1

48
y2 + 44

 

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