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The question asks which method is used to derive the equation of a circle in standard form.

Let's break down the options:

A. **Quadratic formula** - This formula is used to solve quadratic equations, not to derive the equation of a circle. So, this is incorrect.

B. **Completing the square** - This method *is* commonly used to derive the equation of a circle. The general form of a circle's equation is \( x^2 + y^2 + Dx + Ey + F = 0 \), and completing the square on the \(x\)- and \(y\)-terms transforms this into the standard form \( (x - h)^2 + (y - k)^2 = r^2 \), where \((h, k)\) is the center and \(r\) is the radius. So, this is correct.

C. **Distance formula** - The distance formula is used to calculate the distance between two points, but it's not directly used to derive the equation of a circle. This is incorrect.

D. **Midpoint formula** - The midpoint formula is used to find the midpoint between two points, not to derive the equation of a circle. This is incorrect.

**Correct answer: B.** Completing the square is the method used to derive the equation of a circle in standard form.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. How do you complete the square to derive the equation of a circle?
2. What is the general form of a circle's equation before completing the square?
3. How is the center and radius of a circle identified from its equation?
4. Can the distance formula be used to derive the radius of a circle given two points?
5. How does the standard form of a circle’s equation differ from its general form?

**Tip:** When working with equations of circles, always check if you need to complete the square to convert from general form to standard form!

Which statement describes how to derive the equation of a circle in standard form?

Learn how to derive the equation of a circle in standard form using the method of completing the square. This explanation covers the core geometry and algebra concepts involved, making it suitable for students in Grades 9-10.

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