Circle Worksheet
Name_____________________________ Hr____
For each circle below, put the circle in the form
( x − h )2 + ( y − k )2 = r 2 and then
determine the center and radius of the circle.
2
2
2
2
1. x + y − 10x − 2y − 23 = 0
2. x + y − 2x − 8 = 0
2
2
x
+
y
+ 2x + 6y − 6 = 0
3.
2
2
x
+
y
+ 4y − 12 = 0
4.
2
2
x
+
y
− 6x − 10y − 2 = 0
5.
2
2
x
+
y
+ 14x − 12y + 60 = 0
6.
Parabola Worksheet #1
Name_____________________________ Hr____
Determine the vertex, axis of symmetry, and the maximum or minimum value of each parabola.
Also graph each parabola, making a t-table of 5 points.
2
1. y = ( x − 2 ) + 3
2
3. y = 2x − 6
2
2. y = −5 ( x − 1) + 12
2
4. y = 3(x + 5) − 12
2
5. y = 4(x + 6) − 7
2
7. y = x − 6
6. y = −(x + 3)
8. y = −
2
1
( x − 4 )2 + 3
2
Parabola Worksheet #2
Name_____________________________ Hr____
For each problem:
2
a) Put the equation into vertex form: y = a ( x − h ) + k
b)
c)
d)
e)
Find the vertex (h, k)
State the axis of symmetry in equation form x = h
State the maximum or minimum value of the parabola
Graph the parabola making a t-table of 5 points
2
1. y = 2x + 8x − 2
2
2. y = 2x − 12x + 6
2
3. y = −3x + 12x − 1
2
4. y = −x + 6x − 2
2
5. y = 4x + 8x − 5
Parabola Worksheet #3
Name________________________ Hr____
The vertex for all of the following parabolas is (0,0). Given the focus or directrix, find the equation of the
parabola. For each parabola, graph and label the vertex(V), focus(F), directrix(D), & latus rectum endpts (LR).
1. Focus (0, 3)
2. Directrix: y = 6
3. Focus: (0, -4)
4. Focus: (-3. 0)
5. Directrix: x = -6
6. Focus: (4, 0)
7. Directrix: y = -2
8. Focus: (0, 5)
9. Directrix: y = 1
Parabola Worksheet #4
Name_______________________ Hr_____
Determine the equation of each parabola. If not already given, find the vertex, focus, directrix, axis of
symmetry, and latus rectum endpoints of the parabola.
1. Vertex (4, -7); Focus (4, -4)
2. Vertex (-7, 2); Directrix x = -9
3. Vertex (-5, -4); Focus (-8, -4)
4. Focus (-1, -2); Directrix x = 9
5. Vertex (-3, 6); Directrix y = 10
6. Focus (-2, 1); Directrix y = 11
7. Vertex (2, -1); Focus (2, 2)
8. Vertex (-5, -2); Directrix x = -7
9. Vertex (6, -2); Focus (1, -2)
Parabola Worksheet #5
Name______________________ Hr______
Put the following equations in the form y = a(x - h) 2 + k or x = a(y - k)2 + h . Determine the
vertex, focus, directrix, axis of symmetry, and latus rectum endpoints for each parabola.
1. x 2 + 6x + 4y + 5 = 0
2. y 2 - 4y - 16x - 12 = 0
3. x 2 - 4x + 20y + 44 = 0
4. y 2 - 2y - 20x - 119 = 0
5. x 2 + 6x + 16y + 41 = 0
6. y 2 + 8y + 12x - 92 = 0
Ellipse Worksheet #1
Name______________________ Hr______
Determine the center, vertices, foci, and focal constant for each ellipse.
1.
2. 25x 2 + 16y 2 - 1600 = 0
3.
4.
5.
6. 25x 2 + 9y 2 - 2025 = 0
Ellipse Worksheet #2
Name_______________________ Hr_____
Determine the center, vertices, foci, and focal constant for each ellipse.
1. 25x 2 + 9y 2 - 150x + 72y - 3231 = 0
2. 9x 2 + 25y 2 +90x - 300y - 4500 = 0
3. 9x 2 + 4y 2 + 54x - 8y + 49 = 0
4. 9x 2 + 25y 2 - 126x - 300y + 1116 = 0
5. 4x 2 + y 2 + 32x + 4y - 32 = 0
Hyperbola Worksheet #1
Name_______________________ Hr_____
Determine the center, vertices, foci, asymptotes, and focal constant for each hyperbola.
1. x 2 - 4y 2 - 64 = 0
2. 9x 2 - 25y 2 + 900 = 0
3. 25x 2 - 36y 2 + 900 = 0
4.
5.
6. x 2 - 9y 2 - 81 = 0
Hyperbola Worksheet #2
Name__________________________ Hr__
Determine the center, vertices, and foci for each hyperbola.
1. 9x 2 - 4y 2 + 54x + 8y + 41 = 0
2. 9x 2 - 16y 2 + 54x + 128y - 31 = 0
3. 3x 2 - 12y 2 - 18x - 144y - 453 = 0
Conic Sections Review Worksheet
Name______________________ Hr______
For each of the following problems:
Determine what type of conic section it is. GRAPH EVERY PROBLEM. In addition to:
•If it is a circle, find its center and radius.
•If it is a parabola, find its vertex, focus, directrix, axis of symmetry, and LR endpoints.
•If it is an ellipse, find its center, vertices, and foci.
•If it is a hyperbola, find its center, vertices, and foci.
1. x 2 - 4x - 20y - 116 = 0
2. 9x 2 - 16y 2 - 36x - 160y - 508 = 0
3. x 2 + y 2 - 4x + 8y - 29 = 0
4. 16x 2 + 25y 2 - 64x + 50y - 311 = 0
5. 16x 2 - 9y 2 + 32x + 36y + 556 = 0
6. y 2 - 12y + 8x + 84 = 0
7. 25x 2 + 9y 2 - 50x + 54y - 119 = 0
8. x 2 + y 2 + 16x - 10y + 73 = 0
9. y 2 - 12x - 8y + 76 = 0
10. x 2 + 6x + 16y + 105 = 0
11. 9x 2 - y 2 + 108x + 4y + 401 = 0
12. 2x 2 + 2y 2 - 16x + 12y - 78 = 0
13. x 2 + 4x - 8y - 36 = 0
14. 25x 2 + 9y 2 + 300x - 108y + 999 = 0
15. 16x 2 - 9y 2 + 160x + 36y + 220 = 0
16. y 2 - 6y + 16x - 23 = 0
17. 4x 2 + 121y 2 - 8x + 242y - 359 = 0