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  • The equation of the circle described on the common chord of the circles <img alt="\mathrm{x^2+y^2-4 x-5=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E

The equation of the circle described on the common chord of the circles \mathrm{x^2+y^2-4 x-5=0}  and \mathrm{x^2+y^2+8 y+7=0}  as a diameter is
 

Option: 1

\mathrm{( x^2+y^2+2 x+2 y-3=0}


Option: 2

\mathrm{x^2+y^2+4 x-2 y+1=0 }


Option: 3

\mathrm{x^2+y^2-2 x+4 y+1=0}


Option: 4

\mathrm{ x^2+y^2-3 x+2 y-2=0}


Answers (1)

best_answer

equation of common chord \mathrm{S}-\mathrm{S}^1=0=2 \mathrm{y}+\mathrm{x}+3=0 let equation of required circle is \mathrm{x^2+y^2-4 x-5+\lambda(2 y+x+3)=0} centre \mathrm{\left(\frac{4-\lambda}{2},-\lambda\right)} lie on common chord  \mathrm{2 y+x+3=0}

\mathrm{\Rightarrow \lambda=2.}

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