Conic Sections · JEE Advanced previous year questions

2025 1 question

1. Q62025 · 18 May 2025 · Paper 2· One or more correct

   Let $S$ denote the locus of the mid-points of those chords of the parabola $y^2=x$, such that the area of the region enclosed between the parabola and the chord is $\frac{4}{3}$. Let $\mathcal{R}$ denote the region lying in the first quadrant, enclosed by the parabola $y^2=x$, the curve $S$, and the lines $x=1$ and $x=4$. Then which of the following statements is (are) TRUE?

   1. A.$(4,\sqrt{3})\in S$
   2. B.$(5,\sqrt{2})\in S$
   3. C.Area of $\mathcal{R}$ is $\frac{14}{3}-2\sqrt{3}$
   4. D.Area of $\mathcal{R}$ is $\frac{14}{3}-\sqrt{3}$
   Show answer

   Answer: A, C