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A point P moves so that its perpendicular distances from two given lines AB and CD are equal. State the locus of point P.

Locus

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Answer

There can be two cases :

(i) When two lines AB and CD are parallel

In this case the locus of the point P which is equidistant from AB and CD is a line in the midway of AB and CD and parallel to them.

A point P moves so that its perpendicular distances from two given lines AB and CD are equal. State the locus of point P. Locus, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

(ii) When AB and CD are intersecting lines,

In this case the locus of the point P will be a pair of straight lines l and m which bisect the angles between the given lines AB and CD.

A point P moves so that its perpendicular distances from two given lines AB and CD are equal. State the locus of point P. Locus, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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