What is the equation of the circle with centre (,0) and radius 6?
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![### Circle Equation Problem
**Question:**
What is the equation of the circle with center \((\frac{1}{2}, 0)\) and radius 6?
**Answer Choices:**
1. \[
\frac{(2x - 1)^2}{4} + y^2 = 36
\]
2. \[
\frac{(2x - 1)^2}{2} + y^2 = 6
\]
3. \[
\frac{(2x - 1)^2}{4} + y^2 = 6
\]
4. \[
\frac{(2x - 1)^2}{2} + y^2 = 36
\]
### Explanation:
To find the correct equation, recall the standard form of a circle's equation:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle, and \(r\) is the radius.
For this problem:
- The center is \((\frac{1}{2}, 0)\).
- The radius is 6.
Substituting these values into the standard form, we get:
\[
\left(x - \frac{1}{2}\right)^2 + (y - 0)^2 = 6^2
\]
Simplifying further:
\[
\left(x - \frac{1}{2}\right)^2 + y^2 = 36
\]
Checking against the provided answer choices, we see that the correct equation is not present in its simplified form, but an equivalent representation is:
\[
\frac{(2x - 1)^2}{4} + y^2 = 36
\]
Thus, the correct answer is:
\[
\frac{(2x - 1)^2}{4} + y^2 = 36
\]
### Answer:
- The correct option is the first one: \(\boxed{\frac{(2x - 1)^2}{4} + y^2 = 36}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F361784a8-d964-492d-9687-5d5c5e192aef%2F44648aa4-c441-4667-b3e2-aa36b41b8496%2Fx84awf_processed.png&w=3840&q=75)
Transcribed Image Text:### Circle Equation Problem
**Question:**
What is the equation of the circle with center \((\frac{1}{2}, 0)\) and radius 6?
**Answer Choices:**
1. \[
\frac{(2x - 1)^2}{4} + y^2 = 36
\]
2. \[
\frac{(2x - 1)^2}{2} + y^2 = 6
\]
3. \[
\frac{(2x - 1)^2}{4} + y^2 = 6
\]
4. \[
\frac{(2x - 1)^2}{2} + y^2 = 36
\]
### Explanation:
To find the correct equation, recall the standard form of a circle's equation:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle, and \(r\) is the radius.
For this problem:
- The center is \((\frac{1}{2}, 0)\).
- The radius is 6.
Substituting these values into the standard form, we get:
\[
\left(x - \frac{1}{2}\right)^2 + (y - 0)^2 = 6^2
\]
Simplifying further:
\[
\left(x - \frac{1}{2}\right)^2 + y^2 = 36
\]
Checking against the provided answer choices, we see that the correct equation is not present in its simplified form, but an equivalent representation is:
\[
\frac{(2x - 1)^2}{4} + y^2 = 36
\]
Thus, the correct answer is:
\[
\frac{(2x - 1)^2}{4} + y^2 = 36
\]
### Answer:
- The correct option is the first one: \(\boxed{\frac{(2x - 1)^2}{4} + y^2 = 36}\)
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