Conic Sections
Conic Section
star_batch_jee_advanced_2025
Grade None
Question:
A normal drawn to parabola $y^2 = 4ax$ meet the curve again at $Q$ such that angle subtended by $PQ$ at vertex is $90°$, then coordinates of $P$ can be :
(8a, 4\sqrt{2}a)
(8a, 4a)
(2a, -2\sqrt{2}a)
(2a, 2\sqrt{2}a)
Step-by-Step Solution
Key Concept: Chord conditions on a parabola combine parametric relationships with algebraic constraints to determine specific points.
Given $t_2 = -t_1 - \frac{2}{t_1}$ and the product condition $\frac{2at_1}{at_1^2} \cdot \frac{2at_2}{at_2^2} = -1$, we get $t_1 t_2 = -4$. Solving $\frac{-4}{t_1} = -t_1 - \frac{2}{t_1}$ yields $t_1^2 + 2 = 4$, so $t_1 = \pm\sqrt{2}$. The point is $(2a \pm 2\sqrt{2a})$.
Correct Answer: 3,4