Find the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4, x + 2y = 5.

Find the equation of the circle circumscribing the quadrilateral formed by the straight lines : x-y = 0, 3x + 2y = 5, x - y = 10 and 2x + 3y = 0 .

Find the area of the triangle formed by the lines y-x = 0, x + y = 0 and x-k = 0.

Find the co-ordinates of the incentre of the triangle formed by the lines y -15 = 0, 12y - 5x =0 and 4y + 3x =0 .

Find the area of the triangle formed by the lines y-x=0, x+y=0 and x-k=0.

Find the equation of the circle passing through the point of intersection of the circles x^2 + y^2 - 6x + 2y + 4 = 0, x^2 + y^2 + 2x - 4y -6 = 0 and with its centre on the line y = x.

Find the equation of the circle passing through the vertices of the triangle whose sides are : x-y=0, 3x+ 2y = 5 and x + 2y=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 passing through the vertices of the triangle whose sides are : x+y =2, 3x-4y =6 and x-y=0.

Area of the triangle formed by the lines y=2x, y=3x and y=5 is equal to (in square units) :

Using intergration, find the area bounded by the lines : 2x + y = 4, 3x - 2y = 6 and x - 3y + 5 = 0