A) \[\frac{|A{{x}_{1}}+B{{y}_{1}}+C|}{\sqrt{{{A}^{2}}+{{B}^{2}}}}\]
B) \[\frac{|A{{x}_{1}}+B{{y}_{1}}+C|}{\sqrt{A\,\sin \alpha +B\,cos\alpha }}\]
C) \[\frac{|A{{x}_{1}}+B{{y}_{1}}+C|}{|A\,\cos \alpha +B\,sin\alpha |}\]
D) \[\frac{|A{{x}_{1}}+B{{y}_{1}}+C|}{\sqrt{{{A}^{2}}{{\cos }^{2}}\alpha +{{B}^{2}}{{\sin }^{2}}\alpha }}\]
Correct Answer: C
Solution :
[c] Line is passing through the point \[P({{x}_{1}},{{y}_{1}})\] and making an angle a with x-axis. One of the points on this line at distance 'r' from the point P is given by\[({{x}_{1}}+r\cos \alpha ,\,{{y}_{1}}+r\sin \alpha )\]. If this point is Q then it lies on the line \[A({{x}_{1}}+r\cos \alpha )+B({{y}_{1}}+r\sin \alpha )+C=0.\] $\therefore \,\,\,\,r=\frac{|A{{x}_{1}}+B{{y}_{1}}+C|}{|A\cos \alpha +B\sin \alpha |}$
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