question_answer

A straight line passes through a fixed point\[({{x}_{0}},{{y}_{0}})\]. If the equation of the locus of the middle point of it intercepted between the coordinate axes is \[y{{x}_{0}}x{{y}_{0}}=\lambda xy\] (where \[\lambda \in N\]), then \[\lambda \] equals

A)  3                                

B)  1

C)  2                                

D)  4

Correct Answer: C

Solution :

Equation of line \[\frac{x}{2h}+\frac{y}{2k}=1\] passes through    \[({{x}_{0}},\,{{y}_{0}})\] \[\frac{{{x}_{0}}}{2h}+\frac{{{y}_{0}}}{2k}=1\] \[\Rightarrow \]   locus is \[\frac{{{x}_{o}}}{2x}+\frac{{{y}_{o}}}{2y}=1\] \[\Rightarrow \]   \[y{{x}_{o}}+x{{y}_{o}}=2xy\] \[\Rightarrow \]   \[\lambda =2\]