Find the locus of the circumcenter of a triangle whose two sides are along the coordinate axes and the third side passes through the point of intersection of the lines ax+by+c=0 and lx+my+n=0.

Find the locus of the circumcenter of a triangle whose two sides are along the coordinate axes and the third side passes through the point of intersection of the line a x+b y+c=0 and l x+m y+n=0.

If the straight line ax+y+6=0 passes through the point of intersection of the lines x+y+4=0 and 2x+3y+10=0 , find a.

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3).

Find the equation of the hyperbola, whose axes are axes of coordinates and which passes through the points (1,1) and (2,-3).

Find the equation of the hyperbola, whose axes are axes of coordinates and which passes through the point (2,1) and whose eccentricity is sqrt((3)/(2))

Find the centroid of the triangle formed by the line 2x + 3y - 6 = 0, with the coordinate axes.

Find the equation of the hyperboth whose axes are the axes of coordinates and which passes through the points (5,0) and ( -7,(2)/(5) ).

Two equal sides of an isosceles triangle are given by 7x-y+3=0 and x+y=3 , and its third side passes through the point (1,-10) . Find the equation of the third side.

Show that the circle x^(2) + y^(2) + 4(x+y) + 4 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x+y+2 = 0 and which also passes through the origin.