JEE Mains · Maths · STD 11 - 9. straight 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 \(\frac{1}{4}\). 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 ?
- A \(A\) only
- B \(C\) only
- C All the three
- D \(B\) only
Answer & Solution
Correct Answer
(D) \(B\) only
Step-by-step Solution
Detailed explanation
Let the line be \(y=m x+c\) \(x-\)intercept : \(-\frac{ c }{ m }\) \(y-\)intercept : \(C\) \(A.M\) of reciprocals of the intercepts : \(\frac{-\frac{ m }{ c }+\frac{1}{ c }}{2}=\frac{1}{4} \Rightarrow 2(1- m )= c\) line \(: y=m x+2(1-m)=c\) \(\Rightarrow \quad(y-2)-m(x-2)=0\)…
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