A) \[\frac{x}{y}+\frac{y}{3}=-1\]and \[\frac{x}{-2}+\frac{y}{1}=-1\]
B) \[\frac{x}{2}-\frac{y}{3}=-1\]and \[\frac{x}{-2}+\frac{y}{1}=-1\]
C) \[\frac{x}{2}-\frac{y}{3}=1\]and \[\frac{x}{-2}+\frac{y}{1}=1\]
D) \[\frac{x}{y}-\frac{y}{3}=1\]and \[\frac{x}{-2}+\frac{y}{1}=1\]
Correct Answer: D
Solution :
Let a and b intercepts on the coordinate axes. \[\therefore \] \[a+b=-1\Rightarrow b=-(a+1)\] Equation of line is \[\frac{x}{a}+\frac{y}{b}=1\] \[\Rightarrow \] \[\frac{x}{a}-\frac{y}{a+1}=1\] ?(i) Since, this line passes through (4, 3). \[\therefore \] \[\frac{4}{a}-\frac{3}{a+1}=1\Rightarrow a+4={{a}^{2}}+a\] \[\Rightarrow \] \[{{a}^{2}}=4\Rightarrow a=\pm \,2\] \[\therefore \] Equation of line is \[\frac{x}{2}-\frac{y}{3}=1\]or \[\frac{x}{-2}+\frac{y}{1}=1\] [From Eq. (i)]
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