# Rational Equations: ```Module 7 Lesson One Conic Sections
Circles &amp; 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
If you don’t have access to a scanner, you may take snapshots
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
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
3)
x 2  y 2  27
Center (0, 0) Radius 3 3  5.196
5)
( x  1)2  y 2  17
2)
x 2  y 2  100
4)
( x  3)2  ( y  2)2  9
6)
x 2  ( y  6)2  36
Write the equation for the circles shown in each graph.
7)
Center (0, 0) r=6
x&sup2; + y&sup2; = 36
8)
Center (-1, 6) r = 6
(x + 1)&sup2; + (y – 6)&sup2; = 12
9)
Center (3, -1) r = 3
(x – 3)&sup2; + (y + 1) &sup2; = 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.
Radius&sup2; = (5 - -1)&sup2; + (-3 – 4)&sup2; = 6&sup2; + (-7)&sup2; = 85
(x – 5)&sup2; + (y + 3) &sup2; = 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.
r&sup2; = (-2 – 5)&sup2; + (1 – 6)&sup2; = 74
(x + 2)&sup2; + (y – 1)&sup2; = 74
Find the point(s) of intersection of the following systems.
x 2  y 2  16
y  3x  1
&sup2; + (3x + 1)&sup2; = 16
x&sup2; + 9x&sup2; + 6x + 1 = 16
10x&sup2; + 6x – 15 = 0
12)
13)
x 2  ( y  4)2  10
y  x2  1
x&sup2; + (x&sup2; -1 -4)&sup2; = 10
x&sup2; + (x&sup2; - 5)&sup2; = 10
x&sup2; + x4 – 10x&sup2; + 25 = 10
x4 – 9x&sup2; + 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
x&sup2; = 5 𝑦
1
x&sup2; = 4(20) 𝑦
15)
y  3x 2  0
1
x&sup2; = -3y
16) x  9 y 2
1
1
x&sup2; = 4(− 12) 𝑦
y&sup2; = 9x
1
y&sup2; = 4(36) 𝑥
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