JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Area (in sq. units) of the region outside \(\frac{|\mathrm{x}|}{2}+\frac{|\mathrm{y}|}{3}=1\) and inside the ellipse \(\frac{\mathrm{x}^{2}}{4}+\frac{\mathrm{y}^{2}}{9}=1\) is
- A \(3(4-\pi)\)
- B \(6(\pi-2)\)
- C \(3(\pi-2)\)
- D \(6(4-\pi)\)
Answer & Solution
Correct Answer
(B) \(6(\pi-2)\)
Step-by-step Solution
Detailed explanation
\(\frac{|x|}{2}+\frac{|y|}{3}=1\) \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) Area of Ellipse \(=\pi a b=6 \pi\) Required area, \(=\pi \times 2 \times 3-(\) Area of quadrilateral \()\) \(=6 \pi-\frac{1}{2} 6 \times 4\) \(=6 \pi-12\) \(=6(\pi-2)\)
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