Parabola
Parabola
nta_pyq_2025_jan
Grade 11
Question:
If the line 3x - 2y + 12 = 0 intersects the parabola 4y = 3x at the points A and B, then at the vertex of the 2 parabola, the line segment AB subtends an angle equal to
tan -1 ( 4 5 )
tan -1 ( 9 7 )
tan -1 ( 11 9 )
\pi -1 3 - tan ( ) 2 2
Step-by-Step Solution
Key Concept: Apply the core result for parabola parameters and tangents and simplify using the given constraints.
(2) 3x - 2y + 12 = 0 2 4y = 3x 2 \therefore 2(3x + 12) = 3x 2 \Rightarrow x - 2x - 8 = 0 \Rightarrow x = -2, 4 mOA = -3/2, mOB = 3 -3 ⎛ - 3 ⎞ 2 9 tan \theta = = 9 ⎝ 1 - ⎠ 7 2 9 -1 \theta = tan ( ) (angle will be acute) 7
Correct Answer: 2