Module 7 Lesson One Conic Sections
Circles & Parabolas Practice
To complete this assignment, you will need to show how to
graph circles. You have several options to complete this task.
You may complete this assignment by hand (similar to a face to
face class) and scan your assignment in and upload the image.
If you don’t have access to a scanner, you may take snapshots
of your assignment and upload the pictures. Or you may
complete the assignment in a word document and insert your
hand drawn graphs into the document and submit one
document instead of several images. If you need help with
this, please contact me.
When you have completed this assignment please upload your
assignment in the link provided in the course.
Here are the equations for some circles. Graph each circle on
graph paper.
1)
x 2  y 2  16
Center (0, 0) Radius 4
3)
x 2  y 2  27
Center (0, 0) Radius 3 3  5.196
5)
( x  1)2  y 2  17
Center (-1, 0)n Radius 17
2)
x 2  y 2  100
Center (0, 0) Radius 10
4)
( x  3)2  ( y  2)2  9
Center (3, -2) Radius 3
6)
x 2  ( y  6)2  36
Center (0, 6) Radius 6
Write the equation for the circles shown in each graph.
7)
Center (0, 0) r=6
x² + y² = 36
8)
Center (-1, 6) r = 6
(x + 1)² + (y – 6)² = 12
9)
Center (3, -1) r = 3
(x – 3)² + (y + 1) ² = 9
10) A circle has its center at the point (5, -3) and goes through the
point (-1, 4). Give the equation for the circle.
Radius² = (5 - -1)² + (-3 – 4)² = 6² + (-7)² = 85
(x – 5)² + (y + 3) ² = 85
11) A circle has its center at the point (-2, 1) and goes through the
point (5, 6). Give the equation for the circle.
r² = (-2 – 5)² + (1 – 6)² = 74
(x + 2)² + (y – 1)² = 74
Find the point(s) of intersection of the following systems.
Round your answers to 3 decimal places.
x 2  y 2  16
y  3x  1
² + (3x + 1)² = 16
x² + 9x² + 6x + 1 = 16
10x² + 6x – 15 = 0
12)
13)
x 2  ( y  4)2  10
y  x2  1
x² + (x² -1 -4)² = 10
x² + (x² - 5)² = 10
x² + x4 – 10x² + 25 = 10
x4 – 9x² + 15 = 0
(2.606, 5.791) and (1.486, 1.209)
x = 0.961 and x = -1.561
Sub in x-values into y = 3x + 1
(0.961, 3.883) and (-1.561, -3.682)
Write the equation of the parabola in standard form:
14)
y  5x 2
1
x² = 5 𝑦
1
x² = 4(20) 𝑦
15)
y  3x 2  0
1
x² = -3y
16) x  9 y 2
1
1
x² = 4(− 12) 𝑦
y² = 9x
1
y² = 4(36) 𝑥