Find the equation of the circle whose centre is the point of intersection of the lines `2x-3y+4=0and3x+4y-5=0` and passes through the origin.

Find the equation of the plane through the line of intersection of the planes x+2y+3z+4=0 and x-y+z+3=0 and passing through the origin.

Find the vector quation of the plane containing the line of intersection of the planes x-3y+4z-5=0 and 2x-y+3z-1=0 and passing through the point (1,-2,3).

Find the equation of the plane containing the line of intersection of the plane x+y+z-6=0\ a n d\ 2x+3y+4z=5=0 and passing through the point (1, 1,1).

Find the equation of the line passing through the point of intersection of x + 2y =5 and x - 3y = 7, and passing through the point : (0, -1).

Find the equation of the line passing through the point of intersection of the lines x+5y+7=0 and 3x+2y-5=0 (a) parallel to the line 7x+2y-5=0

Find the equation of the line passing through the point of intersection of the lines x+5y+7=0 and 3x+2y-5=0 (b) perpendicular to the line 7x + 2y - 5 = 0

Find the equation of the line passing through the point of intersection of x + 2y =5 and x - 3y = 7, and passing through the point : (2, -3) .

Find the equation of a straight line passing through the point of intersection of the lines : 3x +y-9 =0 and 4x + 3y-7=0 and perpendicular to the line 5x -4y + 1 =0.

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).