Find the equation to the circle whose centre is (2,3) and which passes thorugh the intersection of the lines 3x - 2y -1 = 0 and 4x + y - 27 = 0.

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 whose centre is (2, -3) and which passes through the intersection of the st. lines 3x+2y=11 and 2x+3y=4.

Find the equation of the circle whose centre is the point (1,-2) and which passes through the centre of the circle x^2 + y^2 + 2y = 3 .

Find the equation of the circle having (1,-2) as its centre and passing through the intersection of the lines 3x+y=14 and 2x+5y=18.

Find the equation of the circle, whose centre lies on the line 2x- y- 3 = 0 and which passes through the points (3, - 2) and (-2, 0).

Find the equation of the line perpendicular to the line 2x+y -1 = 0 through the intersection of the lines x+2y -1= 0 and y=x.

Find the equation of the straight line which passes through the intersection of the lines x-y-1=0 a n d 2x-3y+1=0 and parallel (i) x -axis (ii) y -axis (iii) 3x+4y=14.

Find the equation of the circle whose centre lies on the line x-4y = 1 and which passes through the points (3, 7) and (5, 5).

Find the equation of the line passing through the intersection of the lines x + 2y - 3 = 0 and 4x - y + 7 = 0 and which is parallel to 5x - 4y - 20 = 0 .

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.