The area enclosed between the curves `y=ax^2 and x=ay^2(a > 0)` is 1 sq. unit, value of a is `1/sqrt3` (b) `1/2` (c) 1 (d) `1/3`

Explanation

Equation of the given two curves are,

`y = ax^2, x = ay^2`

Intersection points of these two curves will be,

`(1/a,1/a)` and `(0,0)`.

So, area between these two curves will be,

`int_0^(1/a)(sqrt(x/a) - ax^2) dx = 1`

`=>[1/sqrta x^(3/2)/(3/2) - (ax^3)/3]_0^(1/a) = 1`

`=>2/3*1/a^2 - 1/3*1/a^2 = 1`

...