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consider the points A(0,1) and B(2,0) and p be a point on the line 4x+3y+9=0 .what are the coordinates of P such that |PA-PB| is maximum.

consider the points A(0,1) and B(2,0) and p be a point on the line 4x+3y+9=0 .what are the coordinates of P such that |PA-PB| is maximum.

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
Writing the P coordinates in parametric form that is in terms of x and y respectively, we get,
P (x , (4x – 9)/3)
Distance PA => root(x^2 + ((4x – 12)/3)^2)
Distance PB = > root( (x-2)^2 + ((4x-9)/3)^2)
Now, let M = |PA – PB|
= |root(x^2 + ((4x – 12)/3)^2) – root( (x-2)^2 + ((4x-9)/3)^2)|
To maximize this, root( (x-2)^2 + ((4x-9)/3)^2) should be minimized.
and for that root( (x-2)^2 + ((4x-9)/3)^2) = 0
that is (x-2)^2 = 0  and also (4x-9)/3)^2 = 0
            x = 2   and  x = 9/4
Hence, y = -17/3  and y =  -6 respectively.
Tese are the final coordinates.

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