Question

Let R be the region in the first quadrant bounded by the graphs of `(x^2/ 9) + (y^2 /81)=1` and `3x+y=9`, how do you find the area?

Answer 1

`(27/4)(pi-2)` areal units.i

Explanation:

The ellipse and the straight line intersect at B(3, 0) and A(9, 0)
The semi-axes of the ellipse are 9 and 3. Its area is `27pi`
The area of the `triangle OAB = 27/2`.

The area bounded by the line and the ellipse in the first quadrant
= area of the ellipse in the quadrant `-` the areal below the line in the quadrant
= `pi(9)(3)(1/4)-(1/2)(3)(9)`