Question

The distance of a movable point from (3,4) is three times of its distance from (-3,--4). Find its locus.​

Answer 1

Answer:

Let the point be P(h,k)

Given points be A(3,0) and B(0,2)

PA=(h−3)2+(k−0)2PB=(h−0)2+(k−2)2

Given PA=3PB

(h−3)2+(k−0)2=3(h−0)2+(k−2)2(h−3)2+(k−0)2=9((h−0)2+(k−2)2)h2+9−6h+k2=9(h2+k2+4−4k)9h2+9k2+36−36k=h2+9−6h+k28h2+8k