Enter Circle Values
Example Data Table
| Center h | Center k | Radius | Standard Equation | Diameter | Area |
|---|---|---|---|---|---|
| 0 | 0 | 5 | x2 + y2 = 25 | 10 | 78.540 |
| 2 | -3 | 4 | (x - 2)2 + (y + 3)2 = 16 | 8 | 50.265 |
| -1 | 6 | 3 | (x + 1)2 + (y - 6)2 = 9 | 6 | 28.274 |
Formula Used
The calculator uses the standard circle equation: (x - h)2 + (y - k)2 = r2. Here, h is the x-coordinate of the center. k is the y-coordinate of the center. r is the radius. A graph point is created with x = h + r cos θ and y = k + r sin θ.
The general equation is x2 + y2 + Dx + Ey + F = 0. This page calculates D as -2h, E as -2k, and F as h2 + k2 - r2.
How to Use This Calculator
Enter the circle center as h and k. Then enter the radius. Choose an angle step for the coordinate table. Add a sample angle if you want one exact plotted point. Enter a test point to check whether that point is inside, outside, or on the circle. Press the calculate button to view equations, graph bounds, intercepts, and downloads.
Graphing a Circle Guide
What the Calculator Does
A circle graph is built from a center and a fixed radius. Every point on the curve stays the same distance from the center. This calculator turns those values into a usable graph, equation, table, and summary. It is helpful for algebra, coordinate geometry, homework checking, and lesson planning. It also gives export files for records.
Understanding the Center
The center controls the placement of the circle. The value h moves the graph left or right. The value k moves the graph up or down. A center of zero and zero places the circle around the origin. A positive h moves it right. A negative h moves it left. The same idea applies to k on the vertical axis.
Understanding the Radius
The radius controls the size. A larger radius makes a wider circle. The diameter is twice the radius. The calculator also finds area and circumference. These values support graph work and measurement work. The graph bounds show the farthest left, right, top, and bottom points.
Coordinate Points
Coordinate points are created from angles. Each angle gives one point on the circle. Smaller angle steps create more points. Larger steps create a shorter table. The exported table can be used in spreadsheets, notes, or classroom material. It also helps users draw the circle by hand with a clear set of plotted coordinates.
Intercepts and Point Checks
Intercepts show where the circle crosses the axes. Some circles cross both axes. Some cross one axis. Some do not cross either axis. The point checker compares the point distance with the radius. Matching distance means the point is on the circle. A smaller distance means it is inside. A larger distance means it is outside.
FAQs
What is a circle equation?
A circle equation describes every point at a fixed distance from one center. The common form is based on center coordinates and radius.
What does h mean in the formula?
h is the x-coordinate of the circle center. It moves the circle left or right on the coordinate plane.
What does k mean in the formula?
k is the y-coordinate of the center. It moves the circle up or down on the graph.
How is the radius used?
The radius sets the distance from the center to every point on the circle. It also controls diameter, area, and circumference.
Can this calculator show intercepts?
Yes. It checks where the circle crosses the x-axis and y-axis. If no real crossing exists, it says no real intercept.
What does the test point result mean?
The test point result compares point distance with the radius. It tells whether the point is inside, outside, or on the circle.
Why choose an angle step?
The angle step controls coordinate table spacing. A smaller step gives more points. A larger step gives fewer points.
What is exported in the files?
The CSV and PDF files include circle inputs, equations, measurements, intercepts, bounds, and coordinate points for study or records.