Find the center-radius form of the circle with center (- 12, - 5) that passes through the point (- 7,5). The center-radius form of the equation of the circle is (Type an equation. Simplify your answer.)
Find the center-radius form of the circle with center (- 12, - 5) that passes through the point (- 7,5). The center-radius form of the equation of the circle is (Type an equation. Simplify your answer.)
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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![**Problem Statement:**
Find the center-radius form of the circle with center \((-12, -5)\) that passes through the point \((-7, 5)\).
**Solution:**
The center-radius form of the equation of the circle is [ ].
*(Type an equation. Simplify your answer.)*
**Explanation:**
Given the center \((-12, -5)\) and a point \((-7, 5)\) on the circle, you can find the radius by calculating the distance between the center and the given point using the distance formula:
\[
r = \sqrt{(-7 - (-12))^2 + (5 - (-5))^2}
\]
Once you have the radius \(r\), substitute it and the center coordinates into the center-radius equation of a circle:
\[
(x + 12)^2 + (y + 5)^2 = r^2
\]
Simplify your answer to obtain the final equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb57887dd-d509-4aed-af0e-6eb91d213510%2Fc2847c5b-9920-419f-8260-a0e7288fd40c%2F8gn3e3q_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the center-radius form of the circle with center \((-12, -5)\) that passes through the point \((-7, 5)\).
**Solution:**
The center-radius form of the equation of the circle is [ ].
*(Type an equation. Simplify your answer.)*
**Explanation:**
Given the center \((-12, -5)\) and a point \((-7, 5)\) on the circle, you can find the radius by calculating the distance between the center and the given point using the distance formula:
\[
r = \sqrt{(-7 - (-12))^2 + (5 - (-5))^2}
\]
Once you have the radius \(r\), substitute it and the center coordinates into the center-radius equation of a circle:
\[
(x + 12)^2 + (y + 5)^2 = r^2
\]
Simplify your answer to obtain the final equation.
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