Find the equation of the circle circumscribing the triangle formed by the lines L 1-0- L 2-0 and L 3-0A- L1- L2- L3-0B- L1 L2 L3-0C- L12- L22- L32-0D- L1 L2- L2 L3- L3 L1-0

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Circle Inscribing a Triangle Fromed by 3 Given Lines

Find the equa...

Question

Find the equation of the circle circumscribing the triangle formed by the lines $L_{1} = 0, L_{2} = 0$ and $L_{3} = 0$

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Solution

The correct option is B

Family of circles circumscribing a triangle whose sides are $L_{1} = 0, L_{2} = 0$ and $L_{3} = 0$ is

$L_{1} L_{2} + λ L_{2} L_{3} + μ L_{3} L_{1} = 0$ - - - - - - (1)

It is the definition of family of circle & circumscribing a triangle.

Equation (1) is a equation of circle so, it should follow following conditions

(1) coefficient of $x y = 0$

(2) coefficient of $x^{2} =$ coefficient of $y^{2}$

Option B is correct

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Find the equation of the circle circumscribing the triangle formed by the lines L1 = 0, L2 = 0 and L3 = 0

Find the equation of the circle circumscribing the triangle formed by the lines $L_{1} = 0, L_{2} = 0$ and $L_{3} = 0$