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  • A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes . Three stone A,B and

A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes \frac{1}{4} . Three stone 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 man?  
Option: 1 B only
Option: 2 C only
Option: 3 A only
Option: 4 All of three

Answers (1)

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\\\frac{x}{a}+\frac{y}{b}=1\\\\\frac{\mathrm{h}}{\mathrm{a}}+\frac{\mathrm{k}}{\mathrm{b}}=1\\\\\frac{\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{~b}}}{2}=\frac{1}{4}\\\\\therefore \frac{1}{\mathrm{a}}+\frac{1}{\mathrm{~b}}=\frac{1}{2} \quad \ldots \ldots (ii) \\\\\therefore$ Line passes through fixed point (2,2) $($ from (1) and (2)$)$

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Suraj Bhandari

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