CET Karnataka Engineering
CET - Karnataka Engineering Solved Paper-2008
question_answer
A variable line \[\frac{x}{a}+\frac{y}{b}=1\] is such that \[a+b=4\] The locus of the mid point of the portion of the line intercepted between the axes is
A) \[x+y=4\]
B) \[x+y=8\]
C) \[x+y=1\]
D) \[x+y=2\]
Correct Answer:
D
Solution :
Let the coordinate of mid point of AB is \[({{x}_{1}},{{y}_{1}})\]. \[\therefore \] \[{{x}_{1}}=\frac{a+0}{2},{{y}_{1}}=\frac{0+b}{2}\] \[\Rightarrow \] \[a=2{{x}_{1}},b=2{{y}_{1}}\] Given, \[a+b=4\] \[\therefore \] \[2{{x}_{1}}+2{{y}_{1}}=4\] \[\Rightarrow \] \[{{x}_{1}}+{{y}_{1}}=2\] Hence, the locus of the mid point is \[x+y=2\]