Circle Equation Calculator With Endpoints

Circle Equation:

\[ (x - h)^2 + (y - k)^2 = r^2 \]

Where (h,k) is the center and r is the radius

Circle Equation:

Center (h,k):

Radius (r):

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1. What is the Circle Equation?

The standard equation of a circle with center (h,k) and radius r is (x - h)² + (y - k)² = r². Given two endpoints of a diameter, we can find the center (midpoint) and radius (half the distance between points).

2. How Does the Calculator Work?

The calculator uses these formulas:

\[ \text{Center} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] \[ \text{Radius} = \frac{\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}{2} \]

Where:

\( (x_1, y_1) \) — First endpoint coordinates
\( (x_2, y_2) \) — Second endpoint coordinates

3. Importance of Circle Equation

Details: The circle equation is fundamental in geometry, used in physics, engineering, and computer graphics to model circular shapes and motions.

4. Using the Calculator

Tips: Enter the coordinates of two endpoints of a diameter. The calculator will determine the center, radius, and standard equation of the circle.

5. Frequently Asked Questions (FAQ)

Q1: What if I don't have diameter endpoints?
A: You need at least two points on the circle's circumference that form a diameter. Three non-collinear points can also define a circle.

Q2: Does the order of endpoints matter?
A: No, the midpoint and radius calculations are the same regardless of which point you enter first.

Q3: What units should I use?
A: Use consistent units for both coordinates. The equation is unitless but preserves the units of your input.

Q4: Can I use this for 3D circles?
A: No, this is for 2D circles only. For spheres in 3D, you would need a different equation.

Q5: How precise are the results?
A: Results are rounded to 2 decimal places. For exact fractions, use exact coordinates.