Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Problem 6) Write the standard equation of the circle.**
**Explanation:**
The diagram presents a circle centered at the origin (0, 0) on a coordinate plane. The radius of the circle is 6 units. The grid helps visualize and confirm this measurement, as the circle intersects the x-axis and y-axis at the points (6, 0), (-6, 0), (0, 6), and (0, -6).
### Solution:
The standard equation of a circle centered at the origin (h, k) with radius r is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Since the center of the circle is at the origin (0, 0), h and k are both 0. The radius r is 6.
Substituting these values into the standard equation, we get:
\[
(x - 0)^2 + (y - 0)^2 = 6^2
\]
Simplifying, this becomes:
\[
x^2 + y^2 = 36
\]
**Therefore, the standard equation of the circle is:**
\[
x^2 + y^2 = 36
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42779bdc-66e8-47e8-8a59-0cd69b39b8c3%2F0a1c72bf-e8af-4f37-ae47-f2c3f71b5be0%2Fxzfjoo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 6) Write the standard equation of the circle.**
**Explanation:**
The diagram presents a circle centered at the origin (0, 0) on a coordinate plane. The radius of the circle is 6 units. The grid helps visualize and confirm this measurement, as the circle intersects the x-axis and y-axis at the points (6, 0), (-6, 0), (0, 6), and (0, -6).
### Solution:
The standard equation of a circle centered at the origin (h, k) with radius r is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Since the center of the circle is at the origin (0, 0), h and k are both 0. The radius r is 6.
Substituting these values into the standard equation, we get:
\[
(x - 0)^2 + (y - 0)^2 = 6^2
\]
Simplifying, this becomes:
\[
x^2 + y^2 = 36
\]
**Therefore, the standard equation of the circle is:**
\[
x^2 + y^2 = 36
\]
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