The distance between the two points and which lie on such that both the line segments and (where is the point ) subtend angle at the origin, is equal to:

Explanation: Solution 1. Setup the Coordinates Let point be since it lies on . Point is and the origin is . The slope of is . The slope of is . 2. Use the Angle Formula The angle between and is . Using : 3. Solve for Case 1: Case 2: These two values of represent the x-coordinates of points and . So, and . 4. Find the distance Since both points are on the horizontal line , the distance is the difference in x-coordinates: Correct Option: (C)

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JEE 2022 — Mathematics PYQ

JEE | Mathematics | 2022

The distance between the two points $A$ and $A'$ which lie on $y = 2$ such that both the line segments $AB$ and $A'B$ (where $B$ is the point $(2,3)$ ) subtend angle $\frac{\pi}{4}$ at the origin, is equal to:

Choose the correct answer: