find the ratio of the areas into which the curves y²=6x divides the region bounded by x²+y²=16

Equation of the circle is x² + y² = 16 (1)
And the parabolic equation is y² = 6x (2)
Now (1) is a circle with centre O (0,0) and radius of 4 units.
And (2) is a  parabola with with vertex at origin.

= 4/3 ( 8π-√3) sq units.
So the ratio of shaded region area to non-shaded region area is $\frac{4/3(8\mathrm{\pi }-\sqrt{3})}{2({\displaystyle \frac{2}{\sqrt{3}}}+{\displaystyle \frac{8\mathrm{\pi }}{3}})}$ (Ans)
Hope you have got it.