# Find the area of the circle x2 + y2 = 16 which is exterior the parabola y2 = 6x. [CBSE 2012(C)]

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

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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