The focus of the parabola y² = 4x + 16 is the centre of the circle C of radius 5. If the values of λ, for which C passes through the point of intersection of the lines 3x - y = 0 and x + λ y = 4, are λ₁ and λ₂, λ₁ < λ₂, then 12λ₁ + 29λ₂ is equal to:

Unclassified (maths): JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q249

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)

The focus of the parabola

y^2 = 4x + 16

is the centre of the circle

C

of radius 5. If the values of

\lambda

, for which

C

passes through the point of intersection of the lines

3x - y = 0

and

x + \lambda y = 4

, are

\lambda_1

and

\lambda_2

\lambda_1 < \lambda_2

, then

12\lambda_1 + 29\lambda_2

is equal to:

Your answerInteger or decimal