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Equation of a Line Passing through 2 Points

The lines a...

Question

The lines $a x + b y + c = 0,$ $b x + c y + a = 0$ and $c x + a y + b = 0$ are concurrent if

A

\sum a^{3} = 3 a b c

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B

\sum a^{2} = a b c

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C

\sum a^{2} = \sum a b

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D

none of these

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Solution

The correct option is A $\sum a^{3} = 3 a b c$

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Similar questions

Q. Prove that the lines

a x + b y + c = 0, b x + c y + a = 0

c x + a y + b = 0

a^{3} + b^{3} + c^{3} = 3 a b c

a + b + c = 0

Q. If lines ax+by+c=0,bx+cy+a=0 and cx+ay+b=0 are concurrent then

a x + b y + c = 0, b x + c y + a = 0

c x + a y + b = 0 (a \neq b \neq c)

are concurrent, if:

Q. If the lines

a x + b y + c = 0, b x + c y + a = 0

c x + a y + b = 0

be concurrent, then

a x + b y + c = u, b x + c y + a = 0

c x + a y + b = 0 (a \neq b \neq c)

are concurrent:

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Equation of a Line Passing through 2 Points

Standard XII Mathematics

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