Geo5.2.28

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Find the equation of a straight line through the point (2,1) and conjugate to the straight line 9x+2y=1\, w.r.t the ellipse 3x^{2}+2y^{2}=1\,

Let P(x_{1},y_{1})\, be the pole of the given line w.r.t the ellipse.

Therefore,the equation of polar is 3xx_{1}+2yy_{1}-1=0\,

Comparing this with the given line

{\frac  {3x_{1}}{9}}={\frac  {2y_{1}}{2}}={\frac  {1}{1}}\,

x_{1}=3,y_{1}=1\,

The line through (2,1)\, conjugate with the given line passes through the pole (3,1)\,

Hence the equation of the line is y-1={\frac  {1-1}{3-2}}(x-2)\,

y-1=0\,

Main Page:Geometry:The Ellipse