Mathematics
The locus of a point which is equidistant from a given circle consists of:
a pair of circles concentric with the given circle.
a circle concentric with the given circle and inside it.
a circle concentric with the given circle and outside it.
a pair of lines parallel to each other on either side of the centre.
Locus
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Answer
If a point stays at a constant distance (let k) from a given circle, then:
One set of such points lies outside the circle at distance k, forming a circle of radius (R + k).
Another set lies inside the circle at distance k, forming a circle of radius (R − k).
Hence, option 1 is the correct option.
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Related Questions
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.
a line l perpendicular to both AB and CD.
a line l in the midway of AB and CD and parallel to them.
none of these
The locus of a point equidistant from two concentric circles is:
a circle concentric with the given circles and inside the smaller circle.
a circle concentric with the given circles and outside the larger circle.
a circle concentric with the given circles and midway between them.
the common centre of the two circles.
A and B are two fixed points in a plane. Then, the locus of a point P which moves in such a way that PA2 + PB2 = AB2, is:
a square with AB as one of its sides.
a rectangle with AB as one of its sides.
a rhombus with AB as one of its diagonal.
the circumference of a circle with AB as its diameter.
The locus of the tip of the pendulum of a clock is:
a circle
a chord of a circle
an arc of a circle
a diameter of a circle