question_answer

If a line intercepted between the coordinate axes is trisected at a point A(4, 3), which is nearer to x-axis, then its equation is:   [JEE Main Online Paper ( Held On 12 Apirl  2014 )

A) \[4x\text{ }-\text{ }3y\text{ }=\text{ }7\text{ }~\]

B) \[3x\text{ }+\text{ }2y\text{ }=\text{ }18\]

C) \[3x\text{ }+\text{ }8y\text{ }=\text{ }36\]                 

D) \[x\text{ }+\text{ }3y\text{ }=\text{ }13\]

Correct Answer: B

Solution :

A divides CB in 2 : 1 \[\Rightarrow \]\[4=\left( \frac{1\times 0+2\times a}{1+2} \right)=\frac{2a}{3}\] \[\Rightarrow \]\[a=6\]\[\Rightarrow \]coordinate of B is B (6, 0) \[3=\left( \frac{1\times b+2\times 0}{1+2} \right)=\frac{b}{3}\]\[\Rightarrow \] b = 9 and C (0, 9) Slope of line passing through (6, 0), (0, 9) slope, \[m=\frac{9}{-6}=-\frac{3}{2}\] Equation of line \[y-0=\frac{-3}{2}(x-6)\] \[2y-3x+18\] \[3x+2y=18\]