Geo4.127

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(2,1) is one limiting point of a coaxal system of which the radical axis is x+y+4=0\,.Find the other limiting point.

The other limiting point is the image of (2,1) w.r.t x+y+4=0\,

If (x2,y2) is the image of (x1,y1) w.r.t ax+by+c=0\,

we have

{\frac  {x_{2}-x_{1}}{a}}={\frac  {y_{2}-y_{1}}{b}}=-2({\frac  {ax_{1}+by_{1}+c}{a^{2}+b^{2}}})\,

x_{2}-2=-7,y_{2}-1=-7\,

x_{2}=-5,y_{2}=-6\,

Therefore,the other limiting point is (-5,-6).


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