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Question

If M(x,y) is equidistant from A(a+b,ba) and B(ab,a+b), then

A
bx+ay=0
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B
bxay=0
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C
ax+by=0
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D
axby=0
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Solution

The correct option is C bxay=0

Distance between two points =(x2x1)2+(y2y1)2

Given, Distance between the points (x,y);(a+b,ba)= Distance between (x,y);(ab,a+b)

(a+bx)2+(bay)2=(abx)2+(a+by)2

=>(a+bx)2+(bay)2=(abx)2+(a+by)2

=>(a+b)2+x22(a+b)x+(ba)2+y22(ba)y=(ab)2+x22(ab)x+(a+b)2+y22(a+b)y

=>2ax2bx2by+2ay=2ax+2bx2ay2by

=>4bx=4ay

=>bxay=0


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