The coordinates of A at time 't' will be

Let the coordinates of B at time 't' be

(i am purposely not using y(t) you will see why.)

The equation of the line AB at time 't' is given by :

.(do you see why?)

The coordinates of M at time 't' are:

(why?)

The monkey is at a distance of 2t from M so the monkey will be found somewhere on the

circle centred at M and of radius 2t.(make sure you understand why this is so). At the same time the monkey is also on the ladder,that is, the monkey will also be somewhere on line AB. The intersection of the circle (mentioned above in green) and AB will give you the position of the monkey.

The equation of that circle is

.

This will intersect AB at two points. One of these is the position of the monkey. Can you figure out which one.