1. What is the Standard Form of a Circle?

The standard form of a circle equation is \((x - h)^2 + (y - k)^2 = r^2\), where (h, k) represents the center of the circle and r represents the radius. This form clearly shows the geometric properties of the circle.

2. How Does the Calculator Work?

The calculator uses the standard form equation:

Where:

• \( h \) — X-coordinate of the center
• \( k \) — Y-coordinate of the center
• \( r \) — Radius of the circle

Explanation: The equation represents all points (x, y) that are at a distance r from the center point (h, k).

3. Importance of Standard Form

Details: The standard form makes it easy to identify the center and radius of a circle, which is essential for graphing and solving geometric problems involving circles.

4. Using the Calculator

Tips: Enter the center coordinates (h, k) and the radius (r). The radius must be a positive value. The calculator will generate the standard form equation.

5. Frequently Asked Questions (FAQ)

Q1: What if the center is at the origin?
A: If the center is at (0, 0), the equation simplifies to \(x^2 + y^2 = r^2\).

Q2: Can the radius be zero?
A: No, a circle with radius zero is just a point, not a circle.

Q3: How do I convert from general form to standard form?
A: Complete the square for both x and y terms to convert from general form to standard form.

Q4: What's the difference between standard form and general form?
A: Standard form clearly shows the center and radius, while general form is expanded as \(x^2 + y^2 + Dx + Ey + F = 0\).

Q5: Can this calculator handle decimal values?
A: Yes, the calculator accepts decimal values for center coordinates and radius.