Geo4.100

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If the circles x^{2}+y^{2}-8x-6y+21=0\, and x^{2}+y^{2}-2y+c=0\, cut each other ortogonally,find the value of c.

In the given circles

g_{1}=4,g_{2}=0,f_{1}=3,f_{2}=1,c_{1}=21,c_{2}=c\,

The condition for two circles to cut orthogonally is

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

Substituting the values in the condition, we have

2(4)(0)+2(3)(1)=21+c\,

c+21=6\,

c=-15\,

The value of c is -15.

Main Page:Geometry:Circles