1. What is Circle General to Standard Form Conversion?

The calculator converts the general form of a circle equation (x² + y² + Dx + Ey + F = 0) to the more useful standard form ((x - h)² + (y - k)² = r²) that clearly shows the center and radius of the circle.

2. How Does the Calculator Work?

The calculator uses the conversion formulas:

Where:

• \( D, E, F \) — Coefficients from the general form
• \( h, k \) — Coordinates of the circle's center
• \( r \) — Radius of the circle

Explanation: The conversion involves completing the square for both x and y terms in the general equation.

3. Importance of Standard Form

Details: The standard form immediately reveals the circle's center and radius, making it essential for graphing and geometric analysis.

4. Using the Calculator

Tips: Enter the coefficients D, E, and F from your general form equation (x² + y² + Dx + Ey + F = 0). The calculator will output the standard form and geometric properties.

5. Frequently Asked Questions (FAQ)

Q1: What if D² + E² - 4F is negative?
A: This means the equation doesn't represent a real circle (radius would be imaginary).

Q2: How do I get the general form from standard form?
A: Expand (x-h)² + (y-k)² = r² and rearrange to x² + y² - 2hx - 2ky + (h²+k²-r²) = 0.

Q3: What's the difference between general and standard form?
A: Standard form clearly shows center (h,k) and radius r, while general form is better for algebraic manipulations.

Q4: Can this calculator handle decimal coefficients?
A: Yes, the calculator works with both integer and decimal coefficients.

Q5: What if my equation has coefficients on x² and y²?
A: First divide all terms by that coefficient to make them 1 before using this calculator.