Conic Sections Review Yourself
By Easy Worksheet / Period: ______Date: ______
Graph:
1) / (x-2)2 + (y)2 = 1/ 2) / (x+2)2 + (y-1)2 = 3
3) / (x-1)2 + (y)2 = 1
/ 4) / (x-3)2 + (y-1)2 = 4
5) / (x-3)2 + (y+1)2 = 4
/ 6) / (x)2 + (y-3)2 = 1
7) / 9(x-1)2 + 16(y-1)2 = 144
/ 8) / 3(x-1)2 + 4(y+3)2 = 12
9) / (x+1)2
16
/ + / (y)2 / = 1
/ 10) / (x+1)2
9
/ + / (y)2
4
/ = 1
11) / (x-1)2 / + / (y)2
2
/ = 1
/ 12) / (x-2)2 / + / (y-3)2
3
/ = 1
13) / y = 3(x-1)2+1.
/ 14) / y = -(x+1)2-3.
15) / x = -(y+1)2-2.
/ 16) / x = 2(y-3)2.
17) / y = -2(x+2)2+2.
/ 18) / x = -(y)2.
19) / (y-1)2
4
/ − / (x)2
4
/ = 1
/ 20) / (y)2
4
/ − / (x-1)2
4
/ = 1
21) / (y-1)2 / − / (x)2 / = 1
/ 22) / (x)2
4
/ − / (y-1)2 / = 1
23) / (x)2
9
/ − / (y)2
9
/ = 1
/ 24) / (y+1)2 / − / (x-1)2 / = 1
Name that conic:
25) / (x -5)29
/ − / (y + 4)2
16
/ = 1
By Easy Worksheet / 26)
27) / -3x2+2x-3y2-y+15=0
By Easy Worksheet / 28) / (x + 2)2 + (y -4)2 = 9
29) / By Easy Worksheet / 30) / -5x2-3x-3y2+y+18=0
Identify the Conic
31) / 5x2 + 10xy + 5y2 - 8x - 8y - 6 = 0By Easy Worksheet / 32) / 6x2 + 2xy + 5y2 - 2x + 9y + 6 = 0
33) / -xy + 6x - 2y - 4 = 0
By Easy Worksheet / 34) / -3x2 + 6xy - 3y2 - 5x - 4y - 5 = 0
35) / -5x2 - 6xy - 8y2 - 4y = 0
By Easy Worksheet / 36) / -xy - 9x + 4y - 10 = 0
Write the Equation in Standard Form:
37) / -3x2 - 3y2 - 36x - 60y - 405 = 0By Easy Worksheet
By Easy / 38) / 9x2 + 25y2 - 162x + 450y + 2529 = 0
39) / 9x2 - 4y2 + 162x - 8y + 689 = 0
By Easy Worksheet / 40) / -16x2 + 16y2 + 64x - 160y + 592 = 0
41) / 4x2 + y2 - 24x + 4y + 36 = 0
By Easy Worksheet / 42) / 4x2 + 9y2 - 16x - 144y + 556 = 0
43) / 16x2 - 4y2 - 96x + 24y + 44 = 0
By / 44) / 4x2 - 4y2 + 48x + 24y + 92 = 0
45) / -8x2 + 32y2 + 16x + 384y + 1272 = 0
By Easy Worksheet / 46) / -x2 - y2 + 12x + 12y - 68 = 0
47) / -4x2 - 16y2 - 80x - 336 = 0
By Easy Worksheet / 48) / x2 + y2 - 4x - 14y + 37 = 0
Conic Sections Review Yourself
1) (x-2)2 + (y)2 = 1
Take the square root of 1 to get the radius: r = 1.
Solve x-2=0 and y=0 to get the center: (2,0)
First mark a dot at the center (2,0) on the graph.
Next, go up/down/left/right from this center point a distance of 1 and mark a dot at each one of those points.
Finally, connect the dots with a circle to get the following graph:
2) (x+2)2 + (y-1)2 = 3
Take the square root of 3 to get the radius: r = 1.73.
Solve x+2=0 and y-1=0 to get the center: (-2,1)
First mark a dot at the center (-2,1) on the graph.
Next, go up/down/left/right from this center point a distance of 1.73 and mark a dot at each one of those points.
Finally, connect the dots with a circle to get the following graph:
3) (x-1)2 + (y)2 = 1
Take the square root of 1 to get the radius: r = 1.
Solve x-1=0 and y=0 to get the center: (1,0)
First mark a dot at the center (1,0) on the graph.
Next, go up/down/left/right from this center point a distance of 1 and mark a dot at each one of those points.
Finally, connect the dots with a circle to get the following graph:
4) (x-3)2 + (y-1)2 = 4
Take the square root of 4 to get the radius: r = 2.
Solve x-3=0 and y-1=0 to get the center: (3,1)
First mark a dot at the center (3,1) on the graph.
Next, go up/down/left/right from this center point a distance of 2 and mark a dot at each one of those points.
Finally, connect the dots with a circle to get the following graph:
5) (x-3)2 + (y+1)2 = 4
Take the square root of 4 to get the radius: r = 2.
Solve x-3=0 and y+1=0 to get the center: (3,-1)
First mark a dot at the center (3,-1) on the graph.
Next, go up/down/left/right from this center point a distance of 2 and mark a dot at each one of those points.
Finally, connect the dots with a circle to get the following graph:
6) (x)2 + (y-3)2 = 1
Take the square root of 1 to get the radius: r = 1.
Solve x=0 and y-3=0 to get the center: (0,3)
First mark a dot at the center (0,3) on the graph.
Next, go up/down/left/right from this center point a distance of 1 and mark a dot at each one of those points.
Finally, connect the dots with a circle to get the following graph:
7) 9(x-1)2 + 16(y-1)2 = 144
First re-write the problem as:
16
/ + / (y-1)2
9
/ = 1
(a is under the x): Take the square root of 16 to get a: a = 4.
(b is under the y): Take the square root of 9 to get b: b = 3.
Solve x-1=0 and y-1=0 to get the center: (1,1)
First mark a dot at the center (1,1) on the graph.
(a goes left/right): Next, go left/right from this center point a distance of 4 and mark a dot at each one of those points.
(b goes up/down): Next, go up/down from this center point a distance of 3 and mark a dot at each one of those points.
Finally, connect the dots with a ellipse to get the following graph:
8) 3(x-1)2 + 4(y+3)2 = 12
First re-write the problem as:
4
/ + / (y+3)2
3
/ = 1
(a is under the x): Take the square root of 4 to get a: a = 2.
(b is under the y): Take the square root of 3 to get b: b = 1.73.
Solve x-1=0 and y+3=0 to get the center: (1,-3)
First mark a dot at the center (1,-3) on the graph.
(a goes left/right): Next, go left/right from this center point a distance of 2 and mark a dot at each one of those points.
(b goes up/down): Next, go up/down from this center point a distance of 1.73 and mark a dot at each one of those points.
Finally, connect the dots with a ellipse to get the following graph:
9)
16
/ + / (y)2 / = 1
First re-write the problem as:
16
/ + / (y)2
1
/ = 1
(a is under the x): Take the square root of 16 to get a: a = 4.
(b is under the y): Take the square root of 1 to get b: b = 1.
Solve x+1=0 and y=0 to get the center: (-1,0)
First mark a dot at the center (-1,0) on the graph.
(a goes left/right): Next, go left/right from this center point a distance of 4 and mark a dot at each one of those points.
(b goes up/down): Next, go up/down from this center point a distance of 1 and mark a dot at each one of those points.
Finally, connect the dots with a ellipse to get the following graph:
10)
9
/ + / (y)2
4
/ = 1
(a is under the x): Take the square root of 9 to get a: a = 3.
(b is under the y): Take the square root of 4 to get b: b = 2.
Solve x+1=0 and y=0 to get the center: (-1,0)
First mark a dot at the center (-1,0) on the graph.
(a goes left/right): Next, go left/right from this center point a distance of 3 and mark a dot at each one of those points.
(b goes up/down): Next, go up/down from this center point a distance of 2 and mark a dot at each one of those points.
Finally, connect the dots with a ellipse to get the following graph:
11)
2
/ = 1
First re-write the problem as:
1
/ + / (y)2
2
/ = 1
(a is under the x): Take the square root of 1 to get a: a = 1.
(b is under the y): Take the square root of 2 to get b: b = 1.41.
Solve x-1=0 and y=0 to get the center: (1,0)
First mark a dot at the center (1,0) on the graph.
(a goes left/right): Next, go left/right from this center point a distance of 1 and mark a dot at each one of those points.
(b goes up/down): Next, go up/down from this center point a distance of 1.41 and mark a dot at each one of those points.
Finally, connect the dots with a ellipse to get the following graph:
12)
3
/ = 1
First re-write the problem as:
1
/ + / (y-3)2
3
/ = 1
(a is under the x): Take the square root of 1 to get a: a = 1.
(b is under the y): Take the square root of 3 to get b: b = 1.73.
Solve x-2=0 and y-3=0 to get the center: (2,3)
First mark a dot at the center (2,3) on the graph.
(a goes left/right): Next, go left/right from this center point a distance of 1 and mark a dot at each one of those points.
(b goes up/down): Next, go up/down from this center point a distance of 1.73 and mark a dot at each one of those points.
Finally, connect the dots with a ellipse to get the following graph:
13) y = 3(x-1)2+1.
The vertex of the parabola can be found by setting x-1=0 and using 1 for y:(1, 1)
So now we can make a chart, filling in the x value (since that's the squared one, and centering our chart around x = 1
-1 / 13
0 / 4
1 / 1
2 / 4
3 / 13
Since 3 is positive, the graph will open up.
By plugging in these other values of x, we can create the following picture:
14) y = -(x+1)2-3.
The vertex of the parabola can be found by setting x+1=0 and using -3 for y:(-1, -3)
So now we can make a chart, filling in the x value (since that's the squared one, and centering our chart around x = -1
-3 / -7
-2 / -4
-1 / -3
0 / -4
1 / -7
Since - is negative, the graph will open down.
By plugging in these other values of x, we can create the following picture:
15) x = -(y+1)2-2.
The vertex of the parabola can be found by setting y+1=0 and using -2 for x:(-2, -1)
So now we can make a chart, filling in the y value (since that's the squared one, and centering our chart around y = -1
-6 / -3
-3 / -2
-2 / -1
-3 / 0
-6 / 1
Since - is negative, the graph will open to the left.
By plugging in these other values of y, we can create the following picture:
16) x = 2(y-3)2.
The vertex of the parabola can be found by setting y-3=0 and using 0 for x:(0, 3)
So now we can make a chart, filling in the y value (since that's the squared one, and centering our chart around y = 3
8 / 1
2 / 2
0 / 3
2 / 4
8 / 5
Since 2 is positive, the graph will open to the right.
By plugging in these other values of y, we can create the following picture:
17) y = -2(x+2)2+2.
The vertex of the parabola can be found by setting x+2=0 and using 2 for y:(-2, 2)
So now we can make a chart, filling in the x value (since that's the squared one, and centering our chart around x = -2
-4 / -6
-3 / 0
-2 / 2
-1 / 0
0 / -6
Since -2 is negative, the graph will open down.
By plugging in these other values of x, we can create the following picture:
18) x = -(y)2.
The vertex of the parabola can be found by setting y=0 and using 0 for x:(0, 0)
So now we can make a chart, filling in the y value (since that's the squared one, and centering our chart around y = 0
-4 / -2
-1 / -1
0 / 0
-1 / 1
-4 / 2
Since - is negative, the graph will open to the left.
By plugging in these other values of y, we can create the following picture:
19)
4
/ − / (x)2
4
/ = 1
(a is under the x): Take the square root of 4 to get a: a = 2.
(b is under the y): Take the square root of 4 to get b: b = 2.
Solve x=0 and y-1=0 to get the center: (0,1)
First mark a dot at the center (0,1) on the graph.
Some books will reverse the roles of a and b below and divide the hyperbola into two cases. We will not do that because if a is always under the x, no second case is necessary.
(a goes left/right): Next, go left/right from this center point a distance of 2 and mark a dot at each one of those points.
(b goes up/down): Next, go up/down from this center point a distance of 2 and mark a dot at each one of those points.
Now, from the "a" dots, go a distance of 2 up and down as well. This will form a square.
Connect the diagonals of the square with a dotted line (these are the asymptotes)
Since the first variable is a y (the y term is positive), the graph will open up/down. So beginning with the first "a" dots we plotted, create your graph opening to the up and down.
If you are careful to approach the asymptotes and not go over those lines, you will end up with: to get the following graph:
20)
4
/ − / (x-1)2
4
/ = 1
(a is under the x): Take the square root of 4 to get a: a = 2.
(b is under the y): Take the square root of 4 to get b: b = 2.
Solve x-1=0 and y=0 to get the center: (1,0)
First mark a dot at the center (1,0) on the graph.
Some books will reverse the roles of a and b below and divide the hyperbola into two cases. We will not do that because if a is always under the x, no second case is necessary.
(a goes left/right): Next, go left/right from this center point a distance of 2 and mark a dot at each one of those points.
(b goes up/down): Next, go up/down from this center point a distance of 2 and mark a dot at each one of those points.
Now, from the "a" dots, go a distance of 2 up and down as well. This will form a square.
Connect the diagonals of the square with a dotted line (these are the asymptotes)
Since the first variable is a y (the y term is positive), the graph will open up/down. So beginning with the first "a" dots we plotted, create your graph opening to the up and down.
If you are careful to approach the asymptotes and not go over those lines, you will end up with: to get the following graph: