The Equation of Circle from Center and Point Coordinates 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,k) Coordinates of Center of Circle
- (x,y) Coordinates of any Point on Circle
Equation: The tool returns:
- (GE) General form of the equation for the circle in the following format: X2 + bX + Y2 + dY + e = 0
- (R) Radius of Circle
- (C) Circumference of Circle
- (A) Area of Circle
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)`
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- Circumference of Circle - Computes the circumference of a circle given the radius (C = 2 π r).
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- Circle around a Triangle - Computes the radius of a circle that circumscribes a triangle given the length of the three sides (a,b,c) of the triangle.
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- Circle Circumference from Area - Computes the circumference of a circle given the area.
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- Chord Length: Computes the length of a chord in a circle from the radius and height.
- Circle Radius from Chord - Computes the radius of a circle based on the length of a chord and the chord's center height.
- Equation of Circle from Center and Point Coordinates - Develops the general equation of a circle based on the coordinates of the center (h,k) and any point on the circle (x,y).
- Circle with same Perimeter as an Ellipse - Computes the radius of the circle with the same perimeter of an ellipse defined by the semi-major and semi-minor axes.
- Rectangles to Cover a Circle - Computes the number of rectangles needed to minimally cover a circle based on the circle's diameter and the length and width of the rectangles.