The line joining (5,0) to (10cos⁡θ,10sin⁡θ) is divided  internally in the ratio 2:3 at P. The locus of P is

P(h,k) divides A(5,0) and B(10cos⁡θ,10sin⁡θ) internally in  the ratio 2:3 . ∴ 15+20cos⁡θ5,20sin⁡θ5=(h,k)∴ 15+20cos⁡θ=5h and 20sin⁡θ=5k∴ 20cos⁡θ=5h−15 and 20sin⁡θ=5kSquaring and adding, we get 400=(5h−15)2+(5k)2∴  Locus is (x−3)2+y2=16