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Why am I not getting it?

I got this statement from a maths reference book,

"Family of circles circumscribing a triangle whose sides are given by \({ L }_{ 1 }=0, { L }_{ 2 }=0\) & \({ L }_{ 3 }=0 \) is given by : \({ L }_{ 1 }{ L }_{ 2 }+\lambda { L }_{ 2 }{ L }_{ 3 }+\mu { L }_{ 3 }{ L }_{ 1 }=0\) provided co-efficient of \(xy=0\) and co-efficient of \({ x }^{ 2 }\)=co-efficient of \({ y }^{ 2 }\)."

I didn't understand this statement. Intersection of \({ L }_{ 1 }=0,{ L }_{ 2 }=0\) & \({ L }_{ 3 }=0\) gives three unique points and we know that one and only one circle passes though three non-collinear points. So how could a family of circles exist?

Note by Anandhu Raj
8 months, 2 weeks ago

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