Question

Using integration find the area of the region 

{(x, y) : 25x² + 9y² ≤ 225 and 5x + 3y ≥ 15}.

Answer 1

The given region is {(x, y): 25x² + 9y² ≥ 225 and 5x + 3y ≥ 15}

Its corresponding equations are

25x² + 9y² = 225 ⇒ \(\frac{x^2}9+\frac{y^2}{25}=1 \) ......(i)

and 5x + 3y = 15.....(ii)

Obviously: curve (i) is an ellipse with centre at (0,0) and major axis along y- axis (ii) is at straight line. Intersection points of (i) and (ii) are (0, 5) and (3,0).

Shaded region is required region and is given by