Question:

The number of elements in the relation $R=\{(x,y):4x^2+y^2<52,\,x,y\in\mathbb{Z}\}$ is

Step-by-Step Solution

Key Concept: $4x^2+y^2<52\Rightarrow x^2<13\Rightarrow x\in\{-3,-2,-1,0,1,2,3\}$. For each $x$, count $y\in\mathbb{Z}$ with $y^2<52-4x^2$.

77 elements.

Correct Answer: 1