The locus of a moving point 'P' which divides AB internally in the ration `2 : 3`, A being the point (2,3) and B is a moving point on `x+y=6` is :

Options

A. a straight line parallel to `x+y=6`
B. a straight line perpendicular to `x+y=6`
C. a circle with (2,3) as centre
D. a circle of radius `sqrt(2)`

Answer

C

Explanation

`because " "(1)/(cosalpha)=(2-cosbeta)/(2cosbeta-1)implies(1-cosalpha)/(1+cosalpha)=((2-cosbeta)-(2cosbeta-1))/((2-cosbeta)+(2cosbeta-1))` (by componendo and dividendo)
`implies " "(1-cosalpha)/(1+cosalpha)=3((1-cosbeta)/(1+cosbeta))impliestan^(2).(alpha)/(2)=3tan^(2).(beta)/(2)`