A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line…

A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 14. Three stones A,B and C are placed at the points 1,1,2,2 and 4,4 respectively. Then which of these stones is/are on the path of the man?
  1. C only
  2. All the three
  3. B only
  4. A only

Solution

Let the line be y=mx+c
x - intercept : -cm
y - intercept : c

A.M of reciprocals of the intercepts :

-mc+1c2=14 ⇒ 21-m=c

line : y=mx+21-m=c

⇒  y-2-mx-2=0

⇒ line always passes through 2,2

Asked in: JEE Main 2021 (24 Feb Shift 1)

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