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Question

If the equation of the locus of a point equidistant from the points (a1,b1) and (a2,b2) is (a1a2)x+(b1b2)y+c=0
then the value of c is

A
12(a22+b22a21b21)
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B
a21+a22+b21b22
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C
12(a21+a22b21b22)
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D
a21+b22a22b22
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Solution

The correct option is A 12(a22+b22a21b21)
Assume the general point as P(h,k), then the locus is
(ha1)2+(kb1)2=(ha2)2+(kb2)2(a1a2)h+(b1b2)k+12(a22+b22a21b21)=0Comparing it with given locus,c=12(a22+b22a21b21)

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