Mathematics
Locus of the centers of the circles passing through two fixed points A and B is :
a line parallel to line segment AB.
the bisector of the line segment AB.
perpendicular to line segment AB.
perpendicular bisector of line segment AB.
Locus
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Answer
Let O and O' be the center of the circles, passing through points AB.
Steps of construction :
Join AB.
Draw a perpendicular from O to AB and O' to AB.
We know that,
Perpendicular from center to chord bisects it.
Since, both perpendiculars bisects AB.
∴ OO' is a straight line perpendicular to AB and bisecting it.
Hence, Option 4 is the correct option.
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