Geo4.128

From Example Problems
Jump to: navigation, search

Find the other limiting point of the coaxal system of which one limiting point is (3,1) and radical axis isx-y+2=0\,

The other limiting point is the image of (3,1) w.r.t x-y+2=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}}}\,

{\frac  {x_{2}-3}{1}}={\frac  {y_{2}-1}{-1}}=-2{\frac  {3-1+2}{2}}\,

x_{2}-3=-4,1-y_{2}=-4\,

x_{2}=-1,y_{2}=-5\,

Therefore,the other limiting point is (-1,-5).


Main Page:Geometry:Circles