Circle Equation Calculator

About Circle Equation Calculator

Circle equation: standard form (x-h)² + (y-k)² = r². General form: x² + y² + Dx + Ey + F = 0.

How to use this calculator

1. Enter the center coordinates as h and k.
2. Enter the radius r.
3. Use the calculator to get the circle equation in standard form.

The formula explained

• \(x\) = x-coordinate of a point on the circle
• \(y\) = y-coordinate of a point on the circle
• \(h\) = x-coordinate of the center
• \(k\) = y-coordinate of the center
• \(r\) = radius of the circle

Step by step method

1. Start with the standard circle form \(\left(x-h\right)^2+\left(y-k\right)^2=r^2\).
2. Substitute the given center values for h and k.
3. Square the radius to find \(r^2\).
4. Write the completed equation and simplify if needed.

Worked example

Suppose the circle has center \(\left(3,-2\right)\) and radius \(5\).

1. Substitute the center into the standard form: \(\left(x-3\right)^2+\left(y-\left(-2\right)\right)^2=r^2\).
2. Rewrite the y-part as \(\left(y+2\right)^2\).
3. Square the radius: \(5^2=25\).

Tips and common mistakes

• Make sure the signs are handled carefully when the center coordinates are negative.
• The radius must be squared on the right-hand side.
• This calculator gives the standard form of a circle equation, not the expanded form.
• If the center is \(\left(0,0\right)\), the equation simplifies to \(x^2+y^2=r^2\).

Frequently asked questions