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If the sum of the distances of a point f...

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is
(a)a square  (b)  a circle (c) a straight line         (d)  two intersecting lines

A

a square

B

a circle

C

a straight line

D

two intersecting lines

Text Solution

Verified by Experts

The correct Answer is:
A
Let the two perpendicular lines be taken as the coordinates axes. If (h,k) is any point on the locus, then according to the given condition, |h|+|k|=1. Hence, the locus of (h,k) is |x|+|y|=1. This consists of four line segments enclosing a square as shown in the figure.
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CENGAGE PUBLICATION-STRAIGHT LINES-EXERCISE (SINGLE CORRECT ANSWER TYPE)
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  10. The area of a parallelogram formed by the lines a x+-b y+-c=0 is

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  13. Find the sum of the series 1^2-2^2+3^2-4^2+\ldots-{2008}^2+{2009}^2

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  16. The equations of the sided of a triangle are x+y-5=0,x-y+1=0, and y-1=...

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  17. The equations of the sided of a triangle are x+y-5=0,x-y+1=0, and y-1=...

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