Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Find the standard form for the equation of a circle**
The equation is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
The circle has a diameter with endpoints \((-3, -9)\) and \((10, -2)\).
1. Calculate the center \((h, k)\) of the circle:
- The center is the midpoint of the diameter.
- Midpoint formula: \[ \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]
2. Calculate the radius \(r\):
- The radius is half the distance between the endpoints of the diameter.
- Distance formula: \[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
**Solutions:**
\(h =\)
\(k =\)
\(r =\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc41fe58f-b2db-440f-b30c-6e46891d2c1e%2F62a5e03f-eca1-4e1e-915f-28cd1e6c01b7%2F7t568lv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the standard form for the equation of a circle**
The equation is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
The circle has a diameter with endpoints \((-3, -9)\) and \((10, -2)\).
1. Calculate the center \((h, k)\) of the circle:
- The center is the midpoint of the diameter.
- Midpoint formula: \[ \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]
2. Calculate the radius \(r\):
- The radius is half the distance between the endpoints of the diameter.
- Distance formula: \[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
**Solutions:**
\(h =\)
\(k =\)
\(r =\)
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