A) \[{{m}^{2}}=1\]
B) \[{{m}^{2}}=3\]
C) \[{{m}^{2}}=7\]
D) \[2{{m}^{2}}=1\]
Correct Answer: C
Solution :
Joint equation of the lines joining the origin and the point of intersection of the line \[y=mx+2\]and the curve\[{{x}^{2}}+{{y}^{2}}=1\]is \[{{x}^{2}}+{{y}^{2}}={{\left( \frac{y-mx}{2} \right)}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}(4-{{m}^{2}})+2mxy+3{{y}^{2}}=0\] Since, lines are at right angles. \[\therefore \] \[4-{{m}^{2}}+3=0\] \[\Rightarrow \] \[{{m}^{2}}=7\]
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