GATE Electrical 2023 | Question: 32

Question

Consider the following equation in a $2-\text{D}$ real-space. 

$\left|x_{1}\right|^{p}+\left|x_{2}\right|^{p}=1 \text { for } p>0$ 

Which of the following statement(s) is/are true? 

• A. When $p=2$, the area enclosed by the curve is $\pi$.
• B. When $p$ tends to $\infty$, the area enclosed by the curve tends to $4.$
• C. When $p$ tends to $0,$ the area enclosed by the curve is $1.$
• D. When $p=1$, the area enclosed by the curve is $2.$ 

Answer 1

I approached this problem using the graph transformation technique I was able to sketch these graphs



We can see here as we get closer to x -> 1 y will tend to 1 as well hence completing the square
as a result the area would be 4

for p =2 it would be a square of radius 1 

For p = 0 it would flat line so area would be 0

for p =1  it would be a square of sides 1 unit 

Hence the options A,B,D should be correct.

 

Answer 2

Answer is A,B,D