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$The coordinates of a point P on the line 2 x - y + 5 = 0 such that | P A - P B | is maximum$ $where A is (\underline{4} - 2) and B is (2, - 4) will be:$

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(11, 27)

(–11,–17)

(–11, 17)

(0,5)

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detailed solution

Correct option is B

Given points are A(4,-2),B(2,-4) Let P(a,b) be appoint on 2x-y+5=0|PA-PB| will be maximum if P,A and B will be collinear. the determinant ab14-212-41=0⇒a(−2+4)−b(4−2)+1(−16+4)=0⇒a−b−6=0........(1) Since P(a,b) be on the 2x-y+5=0 Hence 2a-b+5=0……(2)Solving (1) & (2), we getP(a,b)=(−11,−17)

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