Geo5.4.11

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

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

Any line parallel to this line is

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

Given this line passes thro' (2,{\frac  {\pi }{3}})\,

Hence

{\frac  {k}{2}}=4\cos {\frac  {\pi }{3}}+{\sqrt  {3}}\sin {\frac  {\pi }{3}}\,

{\frac  {k}{2}}=4({\frac  {1}{2}})+{\sqrt  {3}}({\frac  {{\sqrt  {3}}}{2}})\,

{\frac  {k}{2}}={\frac  {7}{2}}\,

k=7\,

Therefore the required line is

{\frac  {7}{r}}=4\cos \theta +{\sqrt  {3}}\sin \theta \,


Main Page:Geometry:Polar Coordinates