Is there a general equation for a circle with a given chord (and other minimum necessary conditions). In quite a lot of questions, the chord length/equation of chord is given and that of circle is asked. I know there must be minimum three conditions to define a unique circle and a chord might just be two of them but given the length and equation of chord how do I find the coordinates of the end points. More precisely, how do I find the end points of a chord given the equation of circle and chord without actually having to solve them simultaneously, i.e. some quirk from the properties of circles/chords box.
Ps; might sound too vague but bear with me here.