Let the coordinates of point A on X-axis be (a,0) and the coordinates of the point B on y-axis be (0,b)
Hence equation of AB will be
x/a+y/b=1.
The point P(4,5) is on AB, So
4/a+5/b=1.....(1)
Again AP/PB=5/3
=>AP^2/PB^2=25/9
=((a-4)^2+25)/(16+(b-5)^2)=25/9...(2)
We are to solve (1)and (2) to get a and b
We can see by inspection that only the coordinates (32/3,0) and (0,8) are in the satisfying form and the values also satisfy the above two equation.
