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**?

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

There are no comments in this discussion.