Circle Equation from Diameter Endpoints
Calculate circle equations in standard, general, and parametric forms
Enter Diameter Endpoints
First Endpoint (x₁, y₁)
Second Endpoint (x₂, y₂)
Step-by-step Solution
Enter the diameter endpoints to see the step-by-step solution.
Quick Examples
Key Formulas
Midpoint Formula
(h, k) = ((x₁+x₂)/2, (y₁+y₂)/2)
Distance Formula
d = √[(x₂-x₁)² + (y₂-y₁)²]
Standard Form
(x-h)² + (y-k)² = r²
General Form
x² + y² + Dx + Ey + F = 0
Circle Properties
Center is the midpoint of diameter
Radius is half the diameter length
Area = πr²
Circumference = 2πr
All points on circle are equidistant from center
Understanding Circle Equations from Diameter Endpoints
What is a Circle?
A circle is a 2-D closed geometrical shape where all boundary points are equidistant from a fixed center point. When you know the endpoints of a diameter, you can determine the complete equation of the circle.
Three Forms of Circle Equations
- •Standard Form: (x-h)² + (y-k)² = r² - Most intuitive
- •General Form: x² + y² + Dx + Ey + F = 0 - Expanded
- •Parametric: x = h + r·cos(α), y = k + r·sin(α) - For plotting
Solution Process
1. Find Center
Use midpoint formula to find the center coordinates
2. Calculate Radius
Use distance formula to find diameter, then divide by 2
3. Write Equations
Substitute center and radius into different equation forms
Key Insight: The diameter endpoints give you everything needed to completely define the circle - center location and size.