JEE Main 2021 (Online) 24th February Morning ShiftQuestion 1
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 $\frac{1}{4}$. 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 ?
Points and Straight Lines
Solution
Line $\frac xa+\frac yb=1$ with $\frac12(\frac1a+\frac1b)=\frac14\Rightarrow\frac1a+\frac1b=\frac12$. So the point $(2,2)$ satisfies $\frac2a+\frac2b=1$. $(1,1)$ gives $\frac12\ne1$, $(4,4)$ gives $2\ne1$. Only $B$ lies on the path. Option (B).