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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.
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) = 0that is (x-2)^2 = 0 and also (4x-9)/3)^2 = 0 x = 2 and x = 9/4Hence, y = -17/3 and y = -6 respectively.Tese are the final coordinates.
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