A circle has center (5, -4) and radius 8. Which gives the equation for the circle? O A. (K + 5)2 + (y – 4)² = 8 O B. (x- 5)2 + (y + 4)2 = 8 O C. * + 5)2 + v – 4)2 = 64 O D. (x- 5)2 + (v + 4)² = 64
A circle has center (5, -4) and radius 8. Which gives the equation for the circle? O A. (K + 5)2 + (y – 4)² = 8 O B. (x- 5)2 + (y + 4)2 = 8 O C. * + 5)2 + v – 4)2 = 64 O D. (x- 5)2 + (v + 4)² = 64
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
![**Question:**
Which angles are congruent to ∠3?
**Diagram Explanation:**
The diagram shows two parallel lines intersected by a transversal line. The intersection creates eight numbered angles. Specifically, angles 1 through 4 are formed at the intersection of the transversal with the first parallel line, and angles 5 through 8 are formed at the intersection with the second parallel line.
**Answer Choices:**
A. ∠2
B. ∠2, ∠6
C. ∠6
D. ∠2, ∠6, ∠7
**Explanation:**
To find which angles are congruent to ∠3, we apply the properties of parallel lines and transversals. Congruent angles could include corresponding angles, alternate interior angles, or vertical angles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ad90659-623c-4b8b-ba1b-6ebab407ee99%2F77c088f2-4bdd-41a2-a53c-400b3d150880%2Fg9lj9qb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Which angles are congruent to ∠3?
**Diagram Explanation:**
The diagram shows two parallel lines intersected by a transversal line. The intersection creates eight numbered angles. Specifically, angles 1 through 4 are formed at the intersection of the transversal with the first parallel line, and angles 5 through 8 are formed at the intersection with the second parallel line.
**Answer Choices:**
A. ∠2
B. ∠2, ∠6
C. ∠6
D. ∠2, ∠6, ∠7
**Explanation:**
To find which angles are congruent to ∠3, we apply the properties of parallel lines and transversals. Congruent angles could include corresponding angles, alternate interior angles, or vertical angles.
![**Circle Equation Identification Exercise**
**Question:**
A circle has center (5, –4) and radius 8. Which gives the equation for the circle?
**Options:**
- A. \((x + 5)^2 + (y - 4)^2 = 8\)
- B. \((x - 5)^2 + (y + 4)^2 = 8\)
- C. \((x + 5)^2 + (y - 4)^2 = 64\)
- D. \((x - 5)^2 + (y + 4)^2 = 64\)
**Explanation:**
The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Given the center \((5, -4)\), we substitute \(h = 5\) and \(k = -4\). The radius is 8, hence \(r^2 = 64\).
Substituting these values into the standard form equation, we get:
\[
(x - 5)^2 + (y + 4)^2 = 64
\]
Therefore, the correct answer is: **Option D: \((x - 5)^2 + (y + 4)^2 = 64\)**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ad90659-623c-4b8b-ba1b-6ebab407ee99%2F77c088f2-4bdd-41a2-a53c-400b3d150880%2Feg920j3g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Circle Equation Identification Exercise**
**Question:**
A circle has center (5, –4) and radius 8. Which gives the equation for the circle?
**Options:**
- A. \((x + 5)^2 + (y - 4)^2 = 8\)
- B. \((x - 5)^2 + (y + 4)^2 = 8\)
- C. \((x + 5)^2 + (y - 4)^2 = 64\)
- D. \((x - 5)^2 + (y + 4)^2 = 64\)
**Explanation:**
The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Given the center \((5, -4)\), we substitute \(h = 5\) and \(k = -4\). The radius is 8, hence \(r^2 = 64\).
Substituting these values into the standard form equation, we get:
\[
(x - 5)^2 + (y + 4)^2 = 64
\]
Therefore, the correct answer is: **Option D: \((x - 5)^2 + (y + 4)^2 = 64\)**.
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