QJEEM24Maca41: JEE Main 2024 Mathematics - Class 12 JEEM24Maca41 Solution: Three points , are on the parabola . Let be the area of the…

Three points \mathrm{O}(0,0), \mathrm{P}\left(\mathrm{a}, \mathrm{a}^2\right), \mathrm{Q}\left(-\mathrm{b}, \mathrm{b}^2\right), \mathrm{a}>0, \mathrm{~b}>0 , are on the parabola $y=x^2$ . Let $\mathrm{S}_1$ be the area of the region bounded by the line $\mathrm{PQ}$ and the parabola, and $\mathrm{S}_2$ be the area of the triangle $\mathrm{OPQ}$ . If the minimum value of $\frac{\mathrm{S}_1}{\mathrm{~S}_2}$ is $\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$ , then $\mathrm{m}+\mathrm{n}$ is equal to __________.