Parabola
Parabola
nta_pyq_2025_jan
Grade 11
Question:
Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y -axis, respectively. If these parabolas intersects at the points A and B , then (AB) 2 is equal to :
Step-by-Step Solution
Key Concept: Apply the core result for parabola parameters and tangents and simplify using the given constraints.
The parabolas are (3) (x - 4) 2 + (y - 3) 2 = x 2 ...(i) and (x - 4) + (y - 3) = y ... 2 2 2 If point of intersection are A (x , y ) and B (x , y ) By solving (i) and (ii), we get 1 1 2 2 x1 + x2 = 14 and x1 x2 = 25 2 2 (AB) = 2 ((x1 + x2 ) - 4x1 x2 ) = 192
Correct Answer: 3