`Eq = f( "[h,k]", "[x,y]")`

Enter a value for all fields

The General Equation of Circle tool develops the general equation of a circle based on the coordinates of the center (h,k) and any point on the circle (x,y).

INSTRUCTIONS: Enter the following:

• (h) This is the x coordinate of the center of the circle.
• (k) This is the y coordinate of the center of the circle.
• (x) This is the x coordinate of any point on the circle.
• (y) This is the y coordinate of any point on the circle.

Equation: The tool returns the general form of the equation for the circle in the following format:

• X² + bX + Y² + dY + e = 0

To compute the radius of the circle based on the center point and a point on the circle, CLICK HERE.

The Math / Science

The general equation for a circle with (h,k) at the center and a point on (x,y) is:

   `(x-h)^2 + (y-k)^2 = r^2`

where:

   `r = sqrt((x-h)^2 + (y-k)^2)`

Circle Calculators

• Circle Area -  This computes the area of a circle given the radius (A = π r²).
• Segment Area f(r,θ) - This computes the area of an arc segment of a circle given the radius (r) and angle (θ)
• Segment Area f(r,h) - This computes the area of an arc segment of a circle given radius (r) and the depth (h) into the circle.
• Sector Area f(r,Θ)- This computes the area of a sector (pie slice) of a circle given the radius (r) and angle (Θ).
• Area of Annulus- This computes the area of an annulus (ring) given the inner radius (r) and outer radius (R).
• Radius -Center to a Point - This computes the radius of a circle given the center point (h,k) and any other point (x,y) on the circle.
• Circumference -  This computes the circumference of a circle given the radius (C = 2 π r).
• Arc Lengths - This computes the length of a cord segment (arc length) on a circle given the radius (r) and angle (Θ)
• Circle within a Triangle -  This computes the radius of a circle inscribed within a triangle given the length of the three sides (a,b,c) of the triangle.
• Circle around a Triangle - This computes the radius of a circle that circumscribes a triangle given the length of the three sides (a,b,c) of the triangle.
• Radius from Circumference - This computes the radius of a circle given the circumference.
• Circumference from Area - This computes the circumference of a circle given the area.
• Radius from Area - This computes the radius of a circle given the area.
• Radius from Chord-  This computes the radius of a circle based on the length of a chord and the chord's center height.