If 6 a 2 − 3 b 2 − c 2 + 7 ab − a c + 4 b c = 0 then the family of lines a x + b y + c = 0 , ∣ a ∣ + ∣ b ∣  = 0 is concurrent at

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Mathematics - Straight Lines Question with Solution | TestHub

MathematicsStraight LinesConcurrency & Family of LinesMedium2 minQB

MathematicsMediummultiple choice

If $6 a^{2} - 3 b^{2} - c^{2} + 7 ab - a c + 4 b c = 0$ then the family of lines $a x + b y + c = 0, ∣ a ∣ + ∣ b ∣ \neq = 0$ is concurrent at

Options:(select one or more)

Answer:

A, B

Solution:

$(2 a + 3 b - c) (3 a - b + c) = 0 \Rightarrow - 2 a - 3 b + c = 0$ or $3 a - b + c = 0$ , i.e. every line of the family passes through (-2, -3) or (3, -1).

Stream:JEESubject:MathematicsTopic:Straight LinesSubtopic:Concurrency & Family of Lines

⏱ 2mℹ️ Source: QB

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