Find the equation of the circle which passes thorugh (1,-2) and (4,-3), and which has its centre on the straight line 3x + 4y = 7.

Find the equation of the circle, which passes through the points (2, - 3) and (3, - 2) and has its centre on the line 2x-3y = 8.

Find the equation of the circle which passes through points (2,-2) and (3,4) and whose centre lies on the line x + y = 2.

Find the equation of the circle which passes through the points (3,4),(3,-6) and (1,2).

Find the equation of a line which passes through the point (2,3,4) and which has equal intercepts on the axes.

Find the equation of the circle whose centre is (2, -3) and which passes through the intersection of the straight lines 3x-2y=1 and 4x+y = 27.

Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x + y = 16 .

Find the equation ofthe circle passing through the points (2,3) and (-1,1) and whose centre is on the line x-3y- 11 =0 .

Find the equation of the circle passing through the point (2,4) and has its centre at the intersection of x-y =4. and 2x +3y=-7.

Find the equation of the circle, which passes through the origin and cut off equal chords of the length 'a' from the straight lines y= x and y=-x .