Question

A = (1,-1) locus of B is x^2+y^2=16 if P divides AB in the ratio 3:2 then find locus of P

Answer 1

see it will help u..
its not solution. BT by seeing it u can solve
AB2 = (x1 – x2)2 + (x1 – 2x2)2 =  2x12 - 6 x1 x2+  5x22 = 16.

Let the point which divides AB in the ratio 1:2 be X(x,y).

We have  XA2 = (x – x1)2 + (y – x1)2 = x2 + y2+ 2x12 - 2 x1 (x + y) = (4x1/3)2 = 16/9.

Similarly, XB2 = (x – x2)2 + (y – 2x2)2 = x2 + y2+ 5x22 - 2 x2 (x + 2y) = (4x2/3)2 = 64/9.

From the first equation, we have  x2 + y2 = 16/9 - 2x12 + 2 x1 (x + y).

Substituting this in the next equation, we get 16/9 - 2x12 + 2 x1 (x + y) + 5x22 - 2 x2 (x + 2y) = 64/9.

Simplifying this, we have 2(x1 – x2)x -  2(x1 + 2x2)y + 2x12 + 5x22 = 48/9 which is the locus.