Wen we r given to find the equation of a circle thru three given points, we go by the family approach..we tend to form the equation of the circle taking the first two points as the end point of the diameter nd den form a strait line eq..we then take the eq of the circle passing thru their intersection as - C[1] + K L[1]=0..put in the the third point nd get the reqd value...now my qs is how can we tek the first two points to be the end points of the diameter??
1actually you need equations of any two curves passing through the given 2 points. need not even be a circle and a straight line.
we consider the circle with these 2 pts. as diameter nd a straight line to ease up things for us.
for each case you will get a specific 'k'
7Whenever we r given the co-ordinates of 3 points, we must remember that we can form a triangle out of these 3 points. Now for every triangle, we can draw a circle we want to and that circle will be unique passing through those 3 points since its a circumcircle of that triangle.
