QJEEM25Mafded: JEE Main 2025 Mathematics - Class 11 JEEM25Mafded Solution: Let the line x+y=1 meet the circle at the points A and B. If…

By solving $\mathrm{x}=\mathrm{y}$ with circle

We get

$$\begin{array}{rl}& \mathrm{C}(\sqrt{2},\sqrt{2})\\ & \mathrm{D}(-\sqrt{2},-\sqrt{2})\end{array}$$

By solving $\mathrm{x}+\mathrm{y}=1$ with circle $x^2+y^2=4$ we set

$$\mathrm{A}(\frac{1+\sqrt{7}}{2},\frac{1-\sqrt{7}}{2})$$

& $\mathrm{B}\left(\frac{1-\sqrt{7}}{2}, \frac{1+\sqrt{7}}{2}\right)$

$\therefore$ Area of Quadrilateral ACBD

$=2 \times$ Area of $\triangle \mathrm{BCD}$

$$\begin{array}{rl}& =2\times \frac{1}{2}\left|\begin{array}{ccc}\sqrt{2}& \sqrt{2}& 1\\ \frac{1-\sqrt{7}}{2}& \frac{1+\sqrt{7}}{2}& 1\\ -\sqrt{2}& -\sqrt{2}& 1\end{array}\right|\\ & =2\sqrt{14}\end{array}$$