A) \[x+y=0\]
B) \[x+2y\pm \sqrt{2}=0\]
C) \[x+2y\pm \sqrt{5}=0\]
D) \[x+\sqrt{5}y\pm 2=0\]
Correct Answer: C
Solution :
Let the equation of straight line is \[\frac{x}{a}+\frac{y}{b}=1\] ?.(i) Where, a = length of intercept on x-axis and b = length of intercept on y-axis. Now, by condition \[a=2b\,\,\,\,\Rightarrow \,\,\,\,\,b=\frac{a}{2}\] ?.(ii) Also, perpendicular distance From origin to line (i) = 1 \[\Rightarrow \] \[\frac{|0+0+1|}{\sqrt{\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}}}=1\] \[\Rightarrow \] \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=1\] \[\Rightarrow \] \[\frac{1}{{{a}^{2}}}+\frac{4}{{{a}^{2}}}=1\] \[\Rightarrow \] \[{{a}^{2}}=5,\] [from Eq. (ii)] \[\Rightarrow \] \[a=\pm \sqrt{5}\] and \[b=\pm \frac{\sqrt{5}}{2}\] Now, from Eq. (i), we get \[\frac{x}{\pm \,\sqrt{5}}\,\,\pm \,\,\frac{y}{\left( \frac{\sqrt{5}}{2} \right)}=1\] \[\Rightarrow \] \[\frac{x}{(\pm \sqrt{5})}+\frac{2y}{(\pm \sqrt{5})}=1\] \[\Rightarrow \] \[x+2y=\pm \sqrt{5}\] \[\Rightarrow \] \[x+2y\pm \sqrt{5}=0\]
You need to login to perform this action.
You will be redirected in
3 sec
