Answers For Conic
Sections in Standard Form
Mr. Clausen Algebra 2
Parabolas
|
# |
Problem |
Opening |
Width |
Vertex |
Axis |
Focus |
Directrix |
Points |
|
1 |
y = 2(x-3)2 +4 |
Up |
Narrow |
(3,4) |
x = 3 |
(3, 4 1/8) |
y = 3 7/8 |
(4,6) (5,12) (6,22) |
|
2 |
y = 1/2(x+1)2 - 2 |
Up |
Wide |
(-1,-2) |
x = -1 |
(-1, -1 1/2) |
y = -2.5 |
(0,-1.5) (1,0) (2, 2.5) |
|
3 |
y = -4(x – 2) 2 +5 |
Down |
Narrow |
(2,5) |
x = 2 |
(2, 4 15/16) |
y = 5 1/16 |
(3,1) (4,-11) |
|
4 |
y = -1/3(x – 3) 2 +1 |
Down |
Wide |
(3,1) |
x = 3 |
(3, 1/4) |
y = 1.75 |
(4, 2/3) (5, -1/3) (6,-2) |
|
5 |
y = -2(x + 1) 2 -1 |
Down |
Narrow |
(-1,-1) |
x = -1 |
(-1, -1/8) |
y = -7/8 |
(0, -3) (1, -9) (2, -19) |
|
6 |
x = 2/3(y – 1)2 +1 |
Right |
Wide |
(1,1) |
y = 1 |
(1 3/8, 1) |
x = 5/8 |
(1 2/3, 2) (3 2/3, 3) |
|
7 |
x = 4(y – 3)2 - 4 |
Right |
Narrow |
(-4,3) |
y = 3 |
(3 7/8, 3) |
x = -4 1/8 |
(0,4) (12,5) |
|
8 |
x = -2(y + 1)2 +3 |
Left |
Narrow |
(3, -1) |
y = -1 |
(2 7/8, -1) |
x = 3 1/8 |
(1,0) (-5,1) (-15,2) |
|
9 |
x = -1/2(y – 2)2 - 5 |
Left |
Wide |
(-5,2) |
y = 2 |
(-5 1/2, 2) |
x = -4 1/2 |
(-5 1/2, 3) (-7,4) |
|
10 |
x = 3(y + 4)2 +3 |
Right |
Narrow |
(3, -4) |
y = - 4 |
(3 1/12, -4) |
x = 2 11/12 |
(15,-2) (-7, 4) |
Circles
|
# |
Problem |
Center |
Radius |
|
1 |
x2 + y2=36 |
(0,0) |
6 |
|
2 |
x2 + (y-3)2 =16 |
(0,3) |
4 |
|
3 |
(x-2)2 + y2=25 |
(2,0) |
5 |
|
4 |
(x+1)2 + (y-5)2=49 |
(-1,5) |
7 |
|
5 |
(x-3)2 + (y+2)2=81 |
(3,-2) |
9 |
|
6 |
(x+5)2 + (y -1)2 =121 |
(-5,1) |
11 |
|
7 |
(x-3/2)2 + (y + 9/2)2 =16 |
(3/2, -9/2) |
4 |
|
8 |
(x + 1)2 + (y – 1)2 =12 |
(-1,1) |
|
|
9 |
(x -3/4)2 + (y + 1/6)2 = 8 |
(3/4, -1/6) |
|
|
10 |
(x + 10)2 + (y - 5) 2 = 7 |
(-10,5) |
|
Ellipses
|
# |
Problem |
Direction |
Center |
a |
b |
c same direction
as “a” |
Vertices |
Foci |
|
1 |
x2/16 + y2/9=1 |
Horizontal |
(0,0) |
4 (left & right) |
3 (up & down) |
|
(4,0) (-4,0) (0,3) (0,-3) |
(2.6,0) (-2.6,0) |
|
2 |
x2/25 + (y-3)2 /4 =1 |
Horizontal |
(0,3) |
5 (left & right) |
2 (up & down) |
|
(5,3) (-5,3) (0,5) (0,1) |
(4.6,3) (-4.6,3) |
|
3 |
(x+1)2/49 + (y+2)2/25 =1 |
Horizontal |
(-1,-2) |
7 (left & right) |
5 (up & down) |
|
(-8,-2) (6,-2) (-1,3) (-1,-7) |
(-5.9,-2) (3.9,-2) |
|
4 |
(x-4)2/12 + (y+3)2/8 =1 |
Horizontal |
(4,-3) |
(left & right) |
(up & down) |
2 |
(7.5,-3) (0.5,-3) (4, 0.2) (4, -5.8) |
(6,-3) (2,-3) |
|
5 |
x2/4 + y2/25 =1 |
Vertical |
(0,0) |
5 (up & down) |
2 (left & right) |
|
(2,0) (-2,0) (0,5) (0,-5) |
(0,4.6) (0,-4.6) |
|
6 |
(x-3)2/4 + y2/16 =1 |
Vertical |
(3,0) |
4 (up & down) |
2 (left & right) |
|
(5,0) (1,0) (3,4) (3,-4) |
(3, 3.5) (3, -3.5) |
|
7 |
(x+4)2/25 + (y+5)2/36 =1 |
Vertical |
(-4,-5) |
6 (up & down) |
5 (left & right) |
|
(-9,-5) (1,-5) (-4,1) (-4,-11) |
(-4, -8.3) (-4,-1.7) |
|
8 |
(x-2)2/4 + (y+3)2/9 =1 |
Vertical |
(2,-3) |
3 (up & down) |
2 (left & right) |
|
(5,-3) (-1,-3) (2,0) (2,-6) |
(2, -5.2) (2,-0.8) |
3.5
Hyperbolas
|
# |
Problem |
Direction |
Center |
a |
b |
c same direction
as “a” |
Vertices |
Foci |
|
1 |
x2/4 - y2/9=1 |
Horiz |
(0,0) |
2 (left & right) |
3 (up & down) |
|
(2,0) (-2,0) |
(-3.6, 0) (3.6, 0) |
|
2 |
(x+1)2/16 - (y+2)2/9=1 |
Horiz |
(-1,-2) |
4 (left & right) |
3 (up & down) |
5 |
(-5,-2) (3,-2) |
(-6, -2) (4, -2) |
|
3 |
(x-3)2/16 - (y+4) 2/25=1 |
Horiz |
(3,-4) |
4 (left & right) |
5 (up & down) |
|
(-1,-4) (7, -4) |
(-3.4, -4) (9.4, -4) |
|
4 |
(x-2)2/36 - (y+2)2/16=1 |
Horiz |
(2,-2) |
6 (left & right) |
4 (up & down) |
|
(-4,-2) (8,-2) |
(-5.2, -2) (9.2, -2) |
|
5 |
y2/4 - x2/9 =1 |
Vert |
(0,0) |
2 (up & down) |
3 (left & right) |
|
(0,2) (0,-2) |
(0, 3.6) (0, -3.6) |
|
6 |
(y-1)2/9 - (x-2)2/4 = 1 |
Vert |
(2,1) |
3 (up & down) |
2 (left & right) |
|
(2, 4) (2,-2) |
(2, 4.6) (2, -2.6) |
|
7 |
(y+2)2/16 – (x+3)2/25=1 |
Vert |
(-3,-2) |
4 (up & down) |
5 (left & right) |
|
(-3, 2) (-3,-6) |
(-3, 4.4) (-3, -8.4) |
|
8 |
(y-3)2/36 – (x-4)2/25=1 |
Vert |
(4,3) |
6 (up & down) |
5 (left & right) |
|
(4,9) (4,-3) |
(4, 10.8) (4, -4.8) |
