A) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,{{\cos }^{2}}\alpha -{{b}^{2}}\,{{\sin }^{2}}\alpha }}\]
B) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,{{\cos }^{2}}\alpha +{{b}^{2}}\,{{\sin }^{2}}\alpha }}\]
C) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,si{{n}^{2}}\alpha -{{b}^{2}}\,{{\cos }^{2}}\alpha }}\]
D) \[\frac{|ab|}{\sqrt{{{a}^{2}}\,si{{n}^{2}}\alpha +{{b}^{2}}\,{{\cos }^{2}}\alpha }}\]
Correct Answer: D
Solution :
The length of perpendicular from the origin to the line \[\frac{x\,\,\sin \,\alpha }{b}-\frac{y\,\cos \,\alpha }{a}-1=0\] is \[d=\frac{|0-0-1|}{\sqrt{\frac{{{\sin }^{2}}\alpha }{{{b}^{2}}}+\frac{{{\cos }^{2}}\alpha }{{{a}^{2}}}}}\] \[=\frac{|ab|}{\sqrt{{{a}^{2}}\,{{\sin }^{2}}\alpha +{{b}^{2}}{{\cos }^{2}}\alpha }}\]
You need to login to perform this action.
You will be redirected in
3 sec
