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An equatin of the family of circles passing through a given pair of points (x_(1), y _(1))and (x _(2), y _(2)) can be taken ad (x - x _(1)) (x -x _(2))+ (y - y_(1)) (y-y_(2))+ k |{:(x,y,1),(x_(1), y _(1), 1),(x_(2), y_(2), 1):}|=0, k being a real parameter. If a member of this family satisfies some other condition then that enables us to determine k and hence the number. Consider the set S of all possible circles that pass through (4,-3) and (-3,4) and thouch the line x +y -5 sqrt2=0. Then which of the following statements is correct ?

Answer»

S CONSISTS of exactly one circle, having radius 5
S consists of exactly one circle, having radius 10
S consists of exactly two CIRCLES, the ratio of radi being `1:2`
S consists of exactly two circles, the ratio of RADII being `2:3`

Answer :A


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