Q. 375.0( 3 Votes )

Find the area of the circle x2 + y2 = 16 which is exterior the parabola y2 = 6x.

Answer :

The given equations are

x2 + y2 = 16 …(i)


And y2 = 6x …(ii)


On solving the equation (i) and (ii),


Or x2 + 6x = 16


Or x2 + 6x – 16 = 0


Or (x + 8)(x – 2) = 0


Or x = 2 or – 8 is not possible solution


When x = 2, y = ± = ± = ±


Equation (i) is a circle with centre (0, 0) and meets axes at (±4,0), (0,±4)


Equation (ii) represents a parabola with axis as x - axis.


Points of intersection are A () and C (2,)


These are shown in the graph below:



Area bounded by the circle and parabola


= 2[Area (OADO) + Area (ADBA)]










Area of circle = π(r) 2


= π(4)2


= 16π sq. Units


Thus, required area





The area of the circle x2 + y2 = 16 which is exterior the parabola y2 = 6x is



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