Locus: ICSE ML Agrawal

Exercise 14

 Question 1 : A point moves such that its distance from a fixed line AB is always the same. What is the relation between AB and the path travelled by P?

Ans :  Here, it is a set of two lines, l and m, which is parallel to AB and drawn on either side at an equal distance from it.

Q.2  A point P moves so that its perpendicular distance from two given lines AB and CD are equal. State the locus of point P.

Ans :     Case 1) if two lines AB and CD are parallel

            It is a line (l) in the midway of lines AB and CD and is parallel to them.

2a

      

     Case 2) If both AB and CD are intersecting lines

The locus of point P will be l and m, which is a pair of straight lines bisecting the angles between AB and CD.

2b

Q.3  P is a fixed point and a point Q moves such that the distance PQ is constant, what is the locus of the path traced out by point Q?

Ans: The locus of point Q is a circle with P as the centre.

A3

Q.4 (i) AB is a fixed line. State the locus of point P so that ∠APB = 90°.

   (ii) A and B are fixed points. State the locus of point P so that ∠APB = 90°.