Line segment joining `(5, 0)` and `(10 costheta,10 sintheta)` is divided by a point P in ratio `2 : 3` If `theta` varies then locus of P is a ; A) Pair of straight lines B) Straight line C) Circle D) Parabola

Explanation

Let point P be `(h,k)`

Here,`h=(2(10costheta)+3(5))/(2+3)=4 sin theta+ 3`
`k=(2(10sintheta)+3(0))/(2+3)=4 sin theta`
`therefore (h-3)^2+k^2=16`
Therefore, locus of `P(h,k)` is `(x-3)^2+y^2=16`.