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
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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.
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.
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