Parabola
Parabola
nta_pyq_2025_jan
Grade 11
Question:
Let the shortest distance from (a, 0), a > 0, to the parabola y 2 = 4x be 4 . Then the equation of the circle passing through the point (a, 0) and the focus of the parabola, and having its centre on the axis of the parabola is :
x + y - 10x + 9 = 0 2 2
x + y - 6x + 5 = 0 2 2
x + y - 4x + 3 = 0 2 2
x + y - 8x + 7 = 0 2 2
Step-by-Step Solution
Key Concept: Apply the core result for parabola parameters and tangents and simplify using the given constraints.
(2) Normal at P 3 y + tx = 2t + t ↑ (a, 0) 3 at = 2t + t 2 a = 2 + t 2 R (2 + t , 0) 2 PR = 4 \Rightarrow 4 + 4t = 16 2 2 4t = 12 \Rightarrow t = 3 a = 5R(5, 0) Focus (1, 0) (1, 0)&(5, 0) will be tha end pts. of diameter \Rightarrow Eg n of circle is 2 (x - 1)(x - 5) + y = 0 2 2 x + y - 6x + 5 = 0
Correct Answer: 2