Which of the following is the center and radius of the circle? ²+²+4x-14y+46-0 O Center (2,-7);r=7 O Center (-4, 14):-√46 O Center (4, -14); r=48 O Center (-2,7): r-fi
Which of the following is the center and radius of the circle? ²+²+4x-14y+46-0 O Center (2,-7);r=7 O Center (-4, 14):-√46 O Center (4, -14); r=48 O Center (-2,7): r-fi
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Question:
Which of the following is the center and radius of the circle?
\[ x^2 + y^2 + 4x - 14y + 46 = 0 \]
### Answer Choices:
- a) Center (2, −7); \( r = 7 \)
- b) Center (−4, 14); \( r = \sqrt{46} \)
- c) Center (4, −14); \( r = 46 \)
- d) Center (−2, 7); \( r = \sqrt{7} \)
### Explanation:
This question is presented to help understand the standard form of a circle equation and enforces knowledge of how to determine the center and radius of a circle given its equation in general quadratic form.
By completing the square on the equation \( x^2 + y^2 + 4x - 14y + 46 = 0 \), the center and radius can be calculated, and you can use the answer choices provided to match to the correct center and radius.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3b617bc-0d34-47a7-bf50-98a510ba10e9%2F0573b303-a9c9-492b-aad3-f2dd90502480%2Fpodxrp_processed.png&w=3840&q=75)
Transcribed Image Text:### Question:
Which of the following is the center and radius of the circle?
\[ x^2 + y^2 + 4x - 14y + 46 = 0 \]
### Answer Choices:
- a) Center (2, −7); \( r = 7 \)
- b) Center (−4, 14); \( r = \sqrt{46} \)
- c) Center (4, −14); \( r = 46 \)
- d) Center (−2, 7); \( r = \sqrt{7} \)
### Explanation:
This question is presented to help understand the standard form of a circle equation and enforces knowledge of how to determine the center and radius of a circle given its equation in general quadratic form.
By completing the square on the equation \( x^2 + y^2 + 4x - 14y + 46 = 0 \), the center and radius can be calculated, and you can use the answer choices provided to match to the correct center and radius.
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