Geo4.101

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If the circles x^{2}+y^{2}-4x-4y=0\, and x^{2}+y^{2}-kx+2y+4=0\, cut each other ortogonally,find the value of k.

From the given circle equations,

g_{1}=2,g_{2}={\frac  {k}{2}},f_{1}=2,f_{2}=-1,c_{1}=0,c_{2}=4\,

The condition is

2g_{1}g_{2}+2f_{1}f_{2}=c_{1}+c_{2}\,

2(2)({\frac  {k}{2}}+2(2)(-1)=0+4\,

2k-4=4\,

k=4\,

Therefore,the value of k is 4.


Mian Page:Geometry:Circles