A) \[p=c\sqrt{1+{{m}^{2}}}\]
B) \[c=p\sqrt{1+{{m}^{2}}}\]
C) \[cp=\sqrt{1+{{m}^{2}}}\]
D) \[{{p}^{2}}+{{c}^{2}}+{{m}^{2}}=1\]
Correct Answer: B
Solution :
If the given lines represent the same line, then the length of the perpendiculars from the origin to the lines are equal, so that \[\frac{c}{\sqrt{1+{{m}^{2}}}}=\]\[\frac{p}{\sqrt{{{\cos }^{2}}\alpha +{{\sin }^{2}}\alpha }}\] \[\Rightarrow \] \[c=p\sqrt{1+{{m}^{2}}}\].
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