question_answer

The equation of a straight line passing through \[(-3,2)\] and cutting an intercept equal in magnitude but opposite in sign from axis, is given by:

A) \[x-y+5=0\]  

B)        \[x+y-5=0\]

C)        \[~x-y-5=0\]  

D)        \[~x+y+5=0\]

Correct Answer: A

Solution :

The intercept form of equation of equal magnitude but opposite sign is \[\frac{x}{a}+\frac{y}{(-a)}=1\] \[\Rightarrow \]               \[x-y=a\] Since, it is passing through \[(-3,2)\] \[\Rightarrow \]               \[-3-2=a\]\[\Rightarrow \]\[a=-5\] \[\therefore \]  \[x-y=-5\] \[\Rightarrow \]               \[x-y+5=0\] Alternate Solution: Since the required line intercept the coordinate axes in equal magnitude and opposite sign, then the intercepted line make an angle \[{{45}^{o}}\]to the \[x-\]axis. \[\therefore \]Equation of straight line is \[\Rightarrow \]    \[y-2=\tan {{45}^{o}}(x+3)\] \[\Rightarrow \]    \[y-2=x+3\] \[\Rightarrow \]    \[x-y+5=0\]