Name____________________
Conic Sections: Parabolas
Homework
Identify the vertex, focus, and directrix of the graph of each equation. Then sketch the graph.
1. y  8x 2
2. x  2y 2
3. y  16 x 2  0
4. x  5 y 2  0
5. x  1  8 y  2   0
6.  x  3  8 y  2   0
7. x 2  2 x  y  3  0
8. y 2  2 y  x  3  0
2
2
Write an equation of a parabola with the vertex at the origin.
9. focus at  2,0
10. directrix at y  4
Conic Sections: Ellipses
Homework
Find the center, vertices, and foci for each equation of an ellipse. Then graph the ellipse.
x2
x2 y2
1.
2.

1
 y2 1
16 25
36
3.
y2
x2

1
9 100
4.
 x  2 2
4

 y  2 2
16
1
5.
x  22   y  12  1
16
7. 9 x 2  36 x  y 2  4 y  31  0
6. 4 x 2  y 2  49
8. 16 x 2  25 y 2  32 x  50 y  16  0
Write an equation in standard form for each ellipse with center at the origin and with the given characteristics.
9. vertex (0, 2 ); co-vertex (-1, 0)
10. vertex (9, 0 ); co-vertex (0, -6)
Conic Sections: Circles
Homework
Write an equation of a circle with the given center and radius.
1. center  1,0 , radius 6
2. center 0,3 , radius 5
3. center  2,6 , radius 11
Find the center and radius of each circle.
4.
x  32   y  12  169
5. x 2  y 2  18
6. 4 x 2  16 x  4 y 2  16 y  4  0
Use the center and radius to graph each circle.
2
2
7. x  5   y  2   4
8. 3x 2  3 y 2  48  0
9. x 2  8 x  y 2  2 y  1  0
10. x 2  y 2  8 x  4 y  19  0
Conic Sections: Hyperbolas
Homework
Find the center, vertices, and foci of the hyperbola.
1.
 y  6 2   x  2 2
36
49
3. x 2  9 y 2  9
1
2.
x  12   y  52
4
25
1
4. 9 x 2  y 2  36 x  6 y  18  0
Find the center, vertices, and foci of the hyperbola, and then graph using the asymptotes as an
aid.
5.
y2 x2

1
9 25
6.
x2 y2

1
49 36
7.
 y  32  x  22
25
16
9. 4 y 2  36 x 2  144
1
8.
x  12
16
y2

1
4
10. x 2  4 y 2  10 x  24 y  15  0
Conic Sections: Review
Classwork/Homework
Identify the conic section represented by each equation. Write the equation in standard form.
Identify all key points then graph.
1. x 2  8 x  4 y 2  48  0
2. x 2  9 y 2  36 y  45  0
3. x 2  y 2  2 x  10 y  38  0
4. x 2  4 x  y  3
5. x 2  4 y 2  4 x  8 y  4
6. 4 x 2  3 y 2  8x  16  0
Write an equation with the given characteristics:
7. ellipse with center (0, 2) , horizontal major axis with length 6, minor axis of length 4
8. ellipse with center (2, -5), one end of each axis at (2, -9) and (-3, -5)
9. circle with center (6, -1) and radius of 4
10. parabola with vertex at (3, -4) and directrix x = 5