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  • The equation of the circle passing through the point of intersection of the curves <img alt="\mathrm{(2 x+3 y+19)(9 x+6 y-17)=0\: and \: x y=0}" src="https://entrancecorner.oncodecogs.com/gif.latex

The equation of the circle passing through the point of intersection of the curves \mathrm{(2 x+3 y+19)(9 x+6 y-17)=0\: and \: x y=0} is
 

Option: 1

\mathrm{x^2+y^2+137 x+63 y-303=0}

 


Option: 2

\mathrm{4 x^2+4 y^2+137 x+63 y-323=0}
 


Option: 3

\mathrm{18 x^2+18 y^2+137 x+63 y-323=0}
 


Option: 4

None of these


Answers (1)

best_answer

Any curve passing through the point of intersection of the given curves is \mathrm{(2 x+3 y+19)(9 x+6 y-17)+\lambda x y=0}
For it to be circle, coefficient of \mathrm{x^2=} coefficient of \mathrm{y^2} (already satisfied), and

coefficient of \mathrm{ x y=0 }

\mathrm{\Rightarrow \quad(12+27+\lambda)=0 }

\mathrm{ \Rightarrow \quad \lambda=-39 }

Hence option 3 is correct.

 

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Sayak

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