If the angle between the pair of straight lines represented by the equation ${x^2} - 3xy + \lambda {y^2} + 3x - 5y + 2 = 0,$ is ${\rm{ta}}{{\rm{n}}^{ - 1}}\left( {\frac{1}{3}} \right)$, where '$\lambda $' is a non-negative real number. Then, $\lambda $ is

JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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If the angle between the pair of straight lines represented by the equation

{x^2} - 3xy + \lambda {y^2} + 3x - 5y + 2 = 0,

\mathrm{ta}{\mathrm{n}^{ - 1}}\left( {\frac{1}{3}} \right)

, where '

\lambda

' is a non-negative real number. Then,

\lambda

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Correct option: A

Option A (2) is correct because it satisfies the given condition for the angle between the pair of straight lines after substituting the values into the relevant formula and solving the resulting quadratic equation.

JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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