Geo5.2.26

From Example Problems
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Find the pole of the line 21x-16y-12=0\, w.r.t the ellipse 3x^{2}+4y^{2}=12\,

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

Therefore,the equation of the polar w.r.t the given ellipse is

3xx_{1}+4yy_{1}-12=0\,

Comparing the equation with the line 21x-16y-12=0\, we get

{\frac  {3x_{1}}{21}}={\frac  {4y_{1}}{-16}}={\frac  {-12}{-12}}\,

{\frac  {x_{1}}{7}}=1,{\frac  {y_{1}}{-4}}=1\,

x_{1}=7,y_{1}=-4\,

Hence the Pole of the given line is (7,-4).


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