Geo5.4.12

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Find the equation of the line passing thro' (-1,{\frac  {\pi }{2}})\, and parallel to 4=r(2\cos \theta +{\sqrt  {3}}\sin \theta )\,

Given line is {\frac  {4}{r}}=2\cos \theta +{\sqrt  {3}}\sin \theta \,

Any line parallel to the line is

{\frac  {k}{r}}=2\cos \theta +{\sqrt  {3}}\sin \theta \,

Given this line passes thro' (-1,{\frac  {\pi }{2}})\,

Hence

{\frac  {k}{-1}}=2\cos {\frac  {\pi }{2}}+{\sqrt  {3}}\sin {\frac  {\pi }{2}}\,

-k=2(0)+{\sqrt  {3}}\,

k=-{\sqrt  {3}}\,

Therefore the required line is -{\sqrt  {3}}=r(2\cos \theta +{\sqrt  {3}}\sin \theta \,


Main Page:Geometry:Polar Coordinates