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  • Two circles x2+y2=6 and x2+y2?6x+8=0 are given. Then find the equation of the circle through their point of intersection and the point (1,1).

Two circles x2+y2=6 and x2+y2?6x+8=0 are given. Then find the equation of the circle through their point of intersection and the point (1,1).

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C_1:x^2+y^2=6\* C_2:x^2+y^2-6x+8=0\* C_3:C_1+lambda C_2=0\* Rightarrow (x^2+y^2-6)+lambda(x^2+y^2-6x+8)=0\* herefore C_3 ;passes;through;(1,1)\*Rightarrow (1+1-6)+lambda(1+1-6+8)=0\* Rightarrow -4+lambda(4)=0Rightarrow lambda=1\*Rightarrow herefore C_3:(x^2+y^2-6)+(1)(x^2+y^2-6x+8)=0\*Rightarrow C_3:2x^2+2y^2-6x+2=0\* Rightarrow C_3:x^2+y^2-3x+1=0

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Deependra Verma

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