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Find the area of the region .
There are two equations involved in the question,
Represents an ellipse, symmetrical about both axis and cutting x - axis
at B (a,0) and ( – a,0)
Represents the area inside the ellipse
Represents a straight line cutting x - axis at B(a,0)
Represents the area above the straight line.
Form the given these two equations; we get the point of intersections. The points are B(a,0) and A(0,b). These are shown in the graph below
The common area is the smaller area of an ellipse.
A = [Area between the curve (i) and x axis from 0 to a] – [Area between the curve (ii) and x axis from 0 to a]
SO, the required area is square units.