Answers For Conic
Sections in General Form
Mr. Clausen Algebra 2
Parabolas
|
# |
General Form |
Standard Form |
Opening |
Width |
Vertex |
Axis |
Focus |
Directrix |
Points |
|
1 |
y=x2+4x-5 |
|
|
|
|
|
|
|
|
|
2 |
y=x2+2x-3 |
|
|
|
|
|
|
|
|
|
3 |
y=x2+4x+4 |
|
|
|
|
|
|
|
|
|
4 |
y=x2-4 |
|
|
|
|
|
|
|
|
|
5 |
y=x2+3x+2 |
|
|
|
|
|
|
|
|
|
6 |
y=x2-5x+4 |
|
|
|
|
|
|
|
|
|
7 |
y=2x2-3x-2 |
|
|
|
|
|
|
|
|
|
8 |
y= |
|
|
|
|
|
|
|
|
|
9 |
y=x2-x+12 |
|
|
|
|
|
|
|
|
|
10 |
y=2x2-2 |
|
|
|
|
|
|
|
|
|
11 |
x=4y2+4y+1 |
|
|
|
|
|
|
|
|
|
12 |
x= |
|
|
|
|
|
|
|
|
|
13 |
x=2y2+6y+4 |
|
|
|
|
|
|
|
|
|
14 |
x= |
|
|
|
|
|
|
|
|
|
15 |
x= |
|
|
|
|
|
|
|
|
|
16 |
x=4y2-1 |
|
|
|
|
|
|
|
|
|
17 |
x=2y2+3y+1 |
|
|
|
|
|
|
|
|
|
18 |
x=6y2-y-1 |
|
|
|
|
|
|
|
|
|
19 |
x=y2+1 |
|
|
|
|
|
|
|
|
|
20 |
x=y2+6y+5 |
|
|
|
|
|
|
|
|
x2+2x-2
y2+2y+3
y2+1
y+1
y2+y+
Circles
|
# |
General Form |
Standard Form |
Center |
Radius |
|
1 |
x2+y2+2x+6y-6=0 |
(x+1)2+(y+3)2 = 16 |
(-1, -3) |
4 |
|
2 |
x2+y2+2x-10y-10=0 |
(x+1)2+(y-5)2 = 36 |
(-1, 5) |
6 |
|
3 |
x2+y2-9=0 |
(x-0)2+(y-0)2 = 9 |
(0, 0) |
3 |
|
4 |
x2+y2+3x-5y- |
(x+3/2)2+(y-5/2)2 = 9 |
(-3/2, 5/2) |
3 |
|
5 |
x2+y2-10x+4y+20=0 |
(x-5)2+(y+2)2 = 9 |
(5, -2) |
3 |
|
6 |
x2+y2-8x-10y+1=0 |
(x-4)2+(y-5)2 = 40 |
(4, 5) |
|
|
7 |
x2+y2+x-8y+ |
(x+1/2)2 + (y-4)2 = 16 |
(-1/2, 4) |
4 |
|
8 |
-2y=x2+5x+y2+ 3 1/4 |
(x+5/2)2+(y+1)2 = 4 |
(-5/2, -1) |
2 |
|
9 |
-y2=x2-16 |
x2+ y2 = 16 |
(0, 0) |
4 |
|
10 |
2x2+2y2-8=0 |
x2+ y2 = 4 |
(0, 0) |
2 |
=0
=0
Ellipses
|
# |
General Form |
Standard Form |
Direction |
Center |
a Same direction
as ellipse |
b opposite
direction from “a” |
c Same direction as “a” |
Vertices |
Foci |
|
1 |
9x2+16y2-144=0 |
|
Horiz |
(0, 0) |
4 |
3 |
|
(4,0 ) (-4,0 ) (0,3 ) (0,-3 ) |
(2.6,0 ) (-2.6, 0) |
|
2 |
9x2+18x+4y2+16y-11=0 |
|
Vert |
(-1, -2) |
3 |
2 |
|
(-1, 1) (-1, -5) (-3, -2) (1, -2) |
(-1, 0.2) (-1, -4.2) |
|
3 |
16x2+25y2-400=0 |
|
Horiz |
(0, 0) |
5 |
4 |
3 |
(5, 0) (-5, 0) (0, 4) (0, -4) |
(3, 0) (-3, 0) |
|
4 |
4x2+y2-24x+4y+36=0 |
|
Vert |
(3, -2) |
2 |
1 |
|
(3, 0) (3, -4) (2, -2) (4, -2) |
(3, -3.7) (3, -0.3) |
|
5 |
16x2+4y2+48x-32y+36=0
|
|
Vert |
(-1.5, 4) |
4 |
2 |
|
(-1.5, 8) (-1.5, 0) (-3.5, 4) (0.5, 4) |
(-1.5, 7.5) (-1.5, 0.5) |
|
6 |
4x2+25y2+20x-150y+150=0 |
|
Horiz |
(-2.5, 3) |
5 |
2 |
|
(-7.5, 3) (2.5, 3) (-2.5, 5) (-2.5, 1) |
(-7.1, 3) (2.1, 3) |
|
7 |
x2+4y2-2x+8y+1=0 |
|
Horiz |
(1, -1) |
2 |
1 |
|
(-1, -1) (3, -1) (1, 0) (1, -2) |
(2.7, -1) (-0.7, -1) |
|
8 |
x2+9y2-10x+16=0 |
|
Horiz |
(5, 0) |
3 |
1 |
|
(8, 0) (2, 0) (5, 1) (5, -1) |
(7.8, 0) (2.2, 0) |
|
9 |
9x2+4y2+36x+24y+36=0 |
|
Vert |
(-2, -3) |
3 |
2 |
|
(-2, 0) (-2, -6) (0, -3) (-4, -3) |
(-2, -5.2) (-2, -0.8) |
Horiz = Horizontal Vert
= Vertical
Hyperbolas
|
# |
General Form |
Standard Form |
Direction |
Center |
a Same direction
as hyperbola |
b opposite
direction from “a” |
c same direction
as “a” |
Vertices |
Foci |
|
1 |
9x2-4y2+18x-16y-43=0 |
|
Horiz |
( -1, -2) |
2 |
3 |
|
(-3 , -2) (1 , -2) |
(-4.6 , -2) (2.6 , -2) |
|
2 |
4x2-25y2-100=0 |
|
Horiz |
(0 , 0) |
5 |
2 |
|
(-5 , 0) (5 , 0) |
(-5.4 , 0) (5.4 , 0) |
|
3 |
4x2-y2-24x+4y+16=0 |
|
Horiz |
(3, 2) |
2 |
4 |
|
(1 , 2) (5 , 2) |
(-1.5 , 2) (7.5 , 2) |
|
4 |
x2-9y2+4x+18y=14 |
|
Horiz |
(-2 , 1) |
3 |
1 |
|
(-5 , 1) (1 , 1) |
(-5.2 , 1) (1.2 , 1) |
|
5 |
4x2-y2+12x-4y+1=0 |
|
Horiz |
(-1.5, -2) |
1 |
2 |
|
(-2.5 , -2) (-0.5 , -2) |
(-3.7 , -2) (0.7 , -2) |
|
6 |
2x2-8y2+8x-24y-18=0 |
|
Horiz |
(-2 , -1.5) |
2 |
1 |
|
(-4 , -1.5) (0 , -1.5) |
(-4.2 , -1.5) (0.2 , -1.5) |
|
7 |
8x2-2y2+32x-6y+19 |
|
Horiz |
(-2 , -1.5) |
1 |
2 |
|
(-3 , -1.5) (-1 , -1.5) |
(-4.2 , -1.5) (0.2 , -1.5) |
|
8 |
x2-4y2-2x-8y-7=0 |
|
Horiz |
(1 , -1) |
2 |
1 |
|
(-1 , -1) (3 , -1) |
(-1.2 , -1) (3.2 , -1) |
|
9 |
9x2-4y2+36x-24y-36=0 |
|
Horiz |
(-2 , -3) |
2 |
3 |
|
(-4 , -3) (0 , -3) |
(-5.6 , -3) (1.6 , -3) |
=0
3.6Horiz = Horizontal Vert
= Vertical