MHT CET · Maths · Area Under Curves
AOB is the positive quadrant of the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) in which \(\mathrm{OA}=5, \mathrm{OB}=3\). The area between the \(\operatorname{arc} \mathrm{AB}\) and the chord AB of the ellipse in sq.units is
- A \(\frac{3}{5}(\pi-2)\)
- B \(\frac{15}{2}(\pi-2)\)
- C \(\frac{3}{10}(\pi-2)\)
- D \(\frac{15}{4}(\pi-2)\)
Answer & Solution
Correct Answer
(D) \(\frac{15}{4}(\pi-2)\)
Step-by-step Solution
Detailed explanation
Area of elliptic quadrant \( = \frac{1}{4}\pi ab \) \( = \frac{1}{4}\pi (5)(3) = \frac{15\pi}{4} \)
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