Find the area of the region in the first quadrant enclosed by the x - axis, the line y = √3x and the circle x2 + y2 = 16.
To find the area enclosed by
y = √3x ...(i)
x2 + y2 = 16 ...(ii)
On solving the equation (i) and (ii),
Or x2 + = 16
Or 4x2 = 16
Or x2 = 4
Or x =
∴ Y = ±
Equation (i) represents a parabola with vertex (0,0) and axis as x - axis.
Equation (ii) represent axis a circle with centre (4,0) and meets axes at (0,0) and (4,0).
They intersect at A (2,) and C ( – 2, – ).
These are shown in the graph below: -
Area of the region OAB = Area OAC + Area ACB
The area of the region in the first quadrant enclosed by x - axis, the line y = √3x and the circle x2 + y2 = 16 is