A) \[x-y+1=0\]
B) \[x-y+2=0\]
C) \[x+y-1=0\]
D) \[x+y+2=0\]
Correct Answer: A
Solution :
The equation of given straight line is \[y-x+5=0\] \[y=x-5\] ? (i) The equation of any straight line parallel to the given straight line will be \[y=x+c\] \[(\because \,\,m=1)\] ... (ii) This straight line will be tangent to the given hyperbola \[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\] ? (iii) Here,\[{{a}^{2}}=3,\,\,{{b}^{2}}=2\], \[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}\] \[\Rightarrow \] \[{{c}^{2}}=3\cdot 1-2\] \[\Rightarrow \] \[{{c}^{2}}=1\] \[\Rightarrow \] \[c=\pm 1\] Hence, the equation of the required tangent will be \[y=x\pm 1\] \[\Rightarrow \] \[y-x-1=0\]or\[y-x+1=0\] \[\Rightarrow \] \[x-y+1=0\]or\[x-y-1=0\]
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