Question

The ratio in which the area bounded by the curves y² = 8x and x² = 8y is divided by the line x = 2 is ______ 

Options

• 15 : 49

• 13 : 48

• 12 : 37

• None of these

Answer 1

The ratio in which the area bounded by the curves y² = 8x and x² = 8y is divided by the line x = 2 is 15 : 49.

Explanation:

 

The given curves intersect at O(0, 0) and P(8, 8).

A₁ = `int_0^2sqrt(8x) dx - int_0^2 x^2/8 dx`

= `sqrt8[(2x^{3/2})/3]_0^2 - [x^3/24]_0^2`

= 5

A₂ = `int_2^8 sqrt(8x) dx - int_2^8 x^2/8 dx`

= `sqrt8[(2x^{3/2})/3]_2^8 - [x^3/24]_2^8`

= `49/3`

∴ A₁ : A₂ = 5 : `49/3` = 15 : 49