CUET · MATHS · PYQ PAPER 2025
The area of the smaller region of the circle \(x^2+y^2=8\) cut off by the line \(x=2\) is
- A \(2(\pi-2)\) sq units
- B \(8 \pi\) sq units
- C \((3 \pi+2)\) sq units
- D \(2(3 \pi+2)\) sq units
Answer & Solution
Correct Answer
(A) \(2(\pi-2)\) sq units
Step-by-step Solution
Detailed explanation
Radius: \(r = \sqrt{8} = 2\sqrt{2}\) Angle of sector: \(\alpha = \arccos\left(\frac{2}{2\sqrt{2}}\right) = \frac{\pi}{4}\). Total angle \(2\alpha = \frac{\pi}{2}\). Area of sector: \(A_{sector} = \frac{1}{2}r^2 (2\alpha) = \frac{1}{2}(8)\left(\frac{\pi}{2}\right) = 2\pi\).…
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