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Question

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


A

L1 + λL2 + μL3 = 0

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B

L1L2 + λL2L3 + μL3L1 = 0

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C

L1L2L3 = 0

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D

L21+λL22+μL23=0

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Solution

The correct option is B

L1L2 + λL2L3 + μL3L1 = 0


Family of circles circumscribing a triangle whose sides are L1 = 0, L2 = 0 and L3 = 0 is

L1L2 + λL2L3 + μL3L1 = 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 xy = 0

(2) coefficient of x2 =coefficient of y2

Option B is correct


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