In the xy-plane, the parabola with equation y=(x−11)2 intersects the line with equation y=25 at two points, A and B. What is the length of ¯¯¯¯¯¯¯¯AB?
A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is