equation of the cord whose midpoint is ( x,y)

Hello Student

(x-p)^2+(y-q)^2=r^2, let is the equation of circle
(x1,y1), is the midpoint of the chord
let (xa,ya),(xb,yb) are end points of chord
(xa+xb)/2=x1,
(ya+yb)/2=y1
(xa-p)^2+(ya-q)^2=c^2
(2x1-xa-p)^2+(2x1-ya-q)^2=c^2
solving above two equation gives, xa, ya
then equation of chord can be found using this two points.

2nd method,
slop of line joining midpoint and circles is (m1=y1-q/x1-p)
m1*m2=-1;

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty