1. What is Standard to General Form Conversion?

The calculator converts a circle's equation from standard form \((x-h)^2 + (y-k)^2 = r^2\) to general form \(x^2 + y^2 + Dx + Ey + F = 0\). This conversion is useful for various geometric calculations and algebraic manipulations.

2. How Does the Calculator Work?

The calculator performs the following conversion:

Where:

• \( h \) — x-coordinate of center
• \( k \) — y-coordinate of center
• \( r \) — Radius of circle
• \( D = -2h \)
• \( E = -2k \)
• \( F = h^2 + k^2 - r^2 \)

Explanation: The calculator expands the standard form equation and collects like terms to produce the general form.

3. Importance of Circle Equations

Details: Both standard and general forms are important in geometry. Standard form clearly shows the center and radius, while general form is better for algebraic operations and solving systems of equations.

4. Using the Calculator

Tips: Enter the circle's center coordinates (h,k) and radius (r). All values can be any real number, with radius > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between standard and general form?
A: Standard form directly shows the center (h,k) and radius r, while general form is expanded and better for algebraic manipulation.

Q2: Can this calculator work in reverse?
A: No, this only converts standard to general form. A separate calculator would be needed for general to standard form conversion.

Q3: What if my radius is zero?
A: A radius of zero represents a single point (degenerate circle). The calculator requires radius > 0.

Q4: How are negative coefficients handled?
A: The calculator properly formats the equation with appropriate + or - signs between terms.

Q5: Can this be used for other conic sections?
A: No, this is specific to circles. Other conic sections (ellipses, parabolas, hyperbolas) have different standard and general forms.