Find the ratio in which the area bounded by the curves `y^2=12 x and x^2=12 y` is divided by the line `x=3.`

Explanation

`A_(1)="Area bounded by "y^(2)=12x,x^(2)=12y, "and line "x=3`
`=int_(0)^(3)sqrt(12x) dxint_(0)^(3)(x^(2))/(12)dx`
`=sqrt(12)|(2x^(3//2))/(3)|_(0)-|(x^(3))/(36)|_(0)=(45)/(4)` sq. units
`A_(2)="Area bounded by "y^(2)=12x and x^(2)=12y`
`=(16(3)(3))/(3)=48` sq. units
`therefore" Required ratio "=((45)/4)/(48-(45)/(4))=(45)/(147)`