Let be a parabola with focus . Let the tangents to the parabola make an angle of with the line touch the parabola at and . Then the value of for which and are coll inear is:

Any Explanation: Solution 1. Slopes of Tangents ( ): Given line: Angle: Case 1: Case 2: 2. Product of Slopes: 3. Conclusion: Tangents hone par perpendicular hote hain. Parabola ki property hai ki perpendicular tangents ke points of contact ( ) hamesha focus ( ) ke saath collinear hote hain (focal chord). Ye property ki kisi bhi value ( ) ke liye valid hai. Correct Option: (D) Any

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JEE 2022 — Mathematics PYQ

JEE | Mathematics | 2022

Let $P : y^2 = 4ax, a > 0$ be a parabola with focus $S$ . Let the tangents to the parabola $P$ make an angle of $\frac{\pi}{4}$ with the line $y = 3x + 5$ touch the parabola $P$ at $A$ and $B$ . Then the value of $a$ for which $A, B$ and $S$ are collinear is:

Choose the correct answer: