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Converters Constants Calculator Analytical Geometry
Circle Vectors Straight Line Parabola Ellipse Hyperbola
Coordinate Geometry [Triangle] Coordinate Geometry [Quadrilateral]
Operations:
Intersection of two circles
Intersection of a circle and a straight line
Equation of circumcircle of a triangle
Image of a circle
Equation of incircle of a triangle
Equation of excircles of a triangle
Equation of common chord of two circles
Parametric Equation of Circle
Chord of Contact of Circle

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OPERATIONS:

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Intersection of two circles
Intersection of a circle and a straight line
Equation of circumcircle of a triangle
Image of a circle
Equation of incircle of a triangle
Equation of excircles of a triangle
Equation of common chord of two circles
Parametric Equation of Circle
Chord of Contact of Circle
General Info
In Polar Coordinates
From two end-points of the diameter
Passing through three points
Touching both the axes
Passing through the origin
Touching a tangent and passing through a point
Passing through Intersecting point of two circles and another point
Passing through Intersecting point of circle and a straight line and another point
Chord Bisected at a Point
Having a center and a tangent

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Equation of a Circle from its two end points of diameter

A circle has a diameter that is formed on two vertices \((x_1,y_1)\) and \((x_2,y_2)\).
Input these data to find the equation of the circle having the line joining these two points as a diameter:







Theory [Equation of a Circle]

If the circle has \((x_1,y_1)\) and \((x_2,y_2)\) as the two end points of one of its diameter, then the equation of the circle is: $$(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$$ $$\Rightarrow x^2+y^2-(x_1+x_2)x-(y_1+y_2)y+x_1x_2+y_1y_2=0$$

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