JEE MATHEMATICS MCQ: STRAIGHT LINES

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Analyzing +4 | -1

The lines

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

and

c x+a y+b=0

are concurrent only when

View answer and explanation

Correct option: B

a^3+b^3+c^3=3 a b c

Option B (

a^3+b^3+c^3=3 a b c

) is correct because the determinant of the coefficients must be zero for the lines to be concurrent.

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\left\{ {a{t_1}{t_2},\;a\left( {{t_1} + {t_2})\} ,\{ a{t_2}{t_3},a({t_2} + {t_3}} \right)} \right\},\;\left\{ {a{t_3}{t_1},\;a\left( {{t_3} + {t_1}} \right)} \right\}

y = 2\;x + 4

6x = 3y + 5

{x^2} + {y^2} + 2xy - 8ax - 8ay - 9{a^2} = 0

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\left( {{x^2} + 7xy + 2{y^2}} \right)\left( {y - 1} \right) = 0