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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
6 months ago

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