Question
ircles The equation of a circle can be changed from general form to standard form by doing which of the follo A. solving for \( y \) B. completing the squares C. squaring both sides D. solving for \( x \)
Ask by Schofield Weaver. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
To change the equation of a circle from general form to standard form, you should **complete the squares**.
Solution
To convert the equation of a circle from general form to standard form, the correct method is:
**B. completing the squares**
### Explanation:
1. **General Form of a Circle**: The general form of a circle's equation is given by:
\[
Ax^2 + Ay^2 + Bx + Cy + D = 0
\]
where \( A \), \( B \), \( C \), and \( D \) are constants.
2. **Standard Form of a Circle**: The standard form of a circle's equation is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \( (h, k) \) is the center of the circle and \( r \) is the radius.
3. **Completing the Squares**: To convert from the general form to the standard form, you need to rearrange the equation and complete the square for both the \( x \) and \( y \) terms. This process allows you to express the equation in a way that reveals the center and radius of the circle.
Thus, the correct answer is **B. completing the squares**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To change the equation of a circle from general form to standard form, the most effective method is completing the squares. This technique allows you to reorganize the equation into a form that clearly shows the circle's center and radius, making it much easier to graph and understand. When you complete the square for both the \(x\) and \(y\) terms, you ultimately derive the familiar format \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. This makes identifying key properties of the circle a breeze!
