Parabola
Parabola
nta_pyq_2025_jan
Grade 11
Question:
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 + \lambday = 4, are \lambda and \lambda , \lambda < \lambda , then 1 2 1 2 12\lambda1 + 29\lambda2 is equal to ________
Step-by-Step Solution
Key Concept: Apply the core result for parabola parameters and tangents and simplify using the given constraints.
y 2 = 4(x + 4) (15) Equation of circle 2 2 (x + 3) + y = 25 Passes through the point of intersection of two lines 3x - y = 0 and x + \lambday = 4 4 12 ( , ) , we get 3\lambda+1 3\lambda+1 7 \lambda = - ,1 6 12\lambda1 + 29\lambda2 - 14 + 29 = 15
Correct Answer: 15