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Question

If the distance of a given point (α,β) from each of the two straight line y = mx through the origin is d, then (αyβx)2 is equal to


A
x2+y2
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B
d2(x2+y2)
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C
d2
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D
None of these
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Solution

The correct option is D d2(x2+y2)
By given condition
βmα1+m2=d
(βmα)2=d2(1+m)2
(βyxα)2=d2(1+y2x2)   m=yx
(βxyα)2x=d2(x2+y2x2)
(βxyα)2=d2(x2+y2)
(αyβx)2=d2(x2+y2)

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