Question

The circle passing through distinct point (1, t), (t, 1) and ( t, t) for all values of t, passes through the point

Answer 1

Let the equation of the general form of the required circle be x22+ y22+ 2gx + 2fy + c = 0 ……………. (i)According to the problem, the above equation of the circle passes through the points P (x1, y1), Q (x2, y2) and R (x3, y3). Therefore,x1122+ y1122+ 2gx11+ 2fy11+ c = 0 ……………. (ii)x2222+ y222+ 2gx22+ 2fy22+ c = 0 ……………. (iii)and  x3322+ y3322+ 2gx33+ 2fy33+ c = 0 ……………. (iv)Form the above there equations (ii), (iii) and (iv) find the value of g, f and c. Then substituting the values of g, f and c in (i) we can find the required equation of the circle.