Question

Area bounded by the curves satisfying the conditions $\frac{x^2}{25}+\frac{y^2}{36}\le 1\le \frac{x}{5}+\frac{y}{6}$ is given by

• A. $15(\frac{\pi }{2}+1)$ sq.units
• B. $\frac{15}{4}(\frac{\pi }{2}-1)$ sq.units
• C. $30(\pi -1)$ sq.unit
• D. $\frac{15}{2}(\pi -2)$ sq.unit

Answer 1

The correct option is D $\frac{15}{2}(\pi -2)$ sq.unit

Area bound b/w the ellipse and the line
Area of quarter ellipse $=\frac{\pi ab}{4}=\frac{\pi \times 5\times 6}{4}$
Area under the line$=\frac{1}{2}\times 5\times 6=\frac{30}{2}$
Area b/w the two curves $=\frac{15\pi }{2}-\frac{30}{2}=\frac{15}{2}(\pi -2)$