# For points  and  of the coordinate plane, a new distance  is defined by . Let  and . Consider the set of points  in the first quadrant which are equidistant (with respect to the new distance) from  and   The set of points  consists of   a) One straight line only   b) Union of two line segments   c) Union of two infinite rays   d) Union of a line segment of finite length and an infinite ray

## Question ID - 55406 | Toppr Answer For points  and  of the coordinate plane, a new distance  is defined by . Let  and . Consider the set of points  in the first quadrant which are equidistant (with respect to the new distance) from  and   The set of points  consists of   a) One straight line only   b) Union of two line segments   c) Union of two infinite rays   d) Union of a line segment of finite length and an infinite ray

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(d)

Let  be a general point in the first quadrant such that

(i)

[  and  are +ve, point  being in first quadrant]

If , then  lies in region . Then,

If , then  lies in region II. Then,

(not possible)

If  then  lies in region III. Then,

(not possible)

if , then  lies in region IV. Then,

Hence, the required set consists of line segment  of finite lengths as shown in the first region and the ray

in the fourth region

Obviously locus of  is union of line segment and one infinite ray