Mathematics
A point P moves such that its distance from a fixed line AB is always the same. What is the relation between AB and the path traveled by P ?
It is a set of two lines perpendicular to AB.
It is a set of two lines parallel to AB drawn on either side at equal distance from it.
It is a set of two concentric circles.
It is a set of two intersecting lines with AB bisecting the angle between them.
Locus
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Answer
If a point moves so that its distance from a fixed line remains constant, it must stay on two lines that maintain that same constant distance on both sides of the given line. These lines are parallel to the original line AB.
So the path is two parallel lines, each at the given fixed distance from AB.
Hence, option 2 is the correct option.
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Related Questions
The locus of a point which is equidistant from two intersecting lines is the formed by the given lines.
pair of lines bisecting the angles
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none of these
If A and B are two fixed points, then the locus of a point P such that ∠APB = 90°, is the:
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A point P moves so that its perpendicular distance from two given parallel lines AB and CD are equal. Then, the locus of the point P is:
a line l anywhere in between AB and CD and parallel to them.
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The locus of a point equidistant from two concentric circles is:
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a circle concentric with the given circles and outside the larger circle.
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the common centre of the two circles.