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Mathematics - Straight Lines Question with Solution | TestHub

MathematicsStraight LinesConcurrency & Family of LinesMedium2 minQB

MathematicsMediuminteger

Lines $a x + b y + p = 0, x cos α + y sin α - p = 0$ with $p \neq = 0$ , and $x sin α - y cos α = 0$ are concurrent. The first two lines include an angle $π /4$ . Find $a^{2} + b^{2}$ .

Answer:

Solution:

Concurrence gives $1 + a cos α + b sin α = 0$ . The angle condition gives $∣ a cos α + b sin α ∣/ a^{2} + b^{2} = 1/ 2$ , so $1/ a^{2} + b^{2} = 1/ 2$ and $a^{2} + b^{2} = 2$ .

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

⏱ 2mℹ️ Source: QB

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