Question

Let 
\(A1 = {(x,y):|x| <= y^2,|x|+2y≤8} \)
and 
\(A2 = {(x,y) : |x| +|y|≤k}. \)
If 27(Area A₁) = 5(Area A₂), then k is equal to :

Answer 1

Correct Answer: 6

The correct answer is 6

Fig.

Required area (above x-axis)
\(A_1 = 2 \int_{4}^{8} (8 - \frac{x}{2} - \sqrt{x}) \, dx\)
\(= 2 \left(16 - \frac{16}{4} - \frac{8}{3/2}\right) = \frac{40}{3}\)
and 
\(A_2 = 4 \left(\frac{1}{2}. k^2\right) = 2k^2\)

Fig. 

\(\therefore 27 \cdot \frac{40}{3} = 5 \cdot (2k^2)\)
⇒ k = 6 

*A₁

Fig.

Which tends to infinity if not mentioned above x-axis