Let the system of equations: 2x + 3y + 5z = 9, 7x + 3y - 2z = 8, 12x + 3y - (4 + λ)z = 16 - μ have infinitely many solutions. Then the radius of the circle centred at (λ, μ) and touching the line 4x = 3y is:

Matrices and Determinants: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q192

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002

Let the system of equations:

\begin{aligned} 2x + 3y + 5z &= 9, \\ 7x + 3y - 2z &= 8, \\ 12x + 3y - (4 + \lambda)z &= 16 - \mu \end{aligned}

have infinitely many solutions. Then the radius of the circle centred at

(\lambda, \mu)

and touching the line

4x = 3y

is:

JEE Main 2025 · April, Unspecified (session-level dataset) · Q192

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002

Let the system of equations:

\begin{aligned} 2x + 3y + 5z &= 9, \\ 7x + 3y - 2z &= 8, \\ 12x + 3y - (4 + \lambda)z &= 16 - \mu \end{aligned}

have infinitely many solutions. Then the radius of the circle centred at

(\lambda, \mu)

and touching the line

4x = 3y

is: