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  • The equation of the circle passing through (1,1) and the points of intersection of the circles <img alt="\mathrm{S=x^2+y^2+13 x-3 y=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5C

The equation of the circle passing through (1,1) and the points of intersection of the circles \mathrm{S=x^2+y^2+13 x-3 y=0}

and \mathrm{S'=2x^2+2y^2+4 x-7 y-25=0} is

Option: 1

\mathrm{ 4 x^2+4 y^2-30 x-10 y-25=0 }


Option: 2

\mathrm{4 x^2+4 y^2+30 x-13 y-25=0 }


Option: 3

\mathrm{ 4 x^2+4 y^3-17 x+10 y+25=0}


Option: 4

None of these


Answers (1)

best_answer

The circle through the points of intersection of \mathrm{S'=0}
and S = 0 is \mathrm{S'+\lambda\: S=0}

\mathrm{2 x^2+2 y^2+4 x-7 y-25+\lambda\left(x^2+y^2+13 x-3 y\right)=0}

It passes through (1, 1).

\mathrm{\begin{aligned} & \therefore \quad 2+2+4-7-25+\lambda(1+1+13-3)=0 \\ & \Rightarrow \lambda=2 \\ & \therefore \quad 2 x^2+2 y^2+4 x-7 y-25+2\left(x^2+y^2+13 x-3 y\right)=0 \\ & \text { or, } 4 x^2+4 y^2+30 x-13 y-25=0 . \end{aligned}}

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rishi.raj

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