Question

Consider the following relations in the real numbers
$R_1=\left\{\left(x,y\right)\right\}|x^2+y^2\le 25$ }
$R_2=\left\{\left(x,y\right)y\ge \frac{4x^2}{9}\right\}$
then the range of $R_1$ $\cap$ $R_2$ is

• A. [0,5]
• B. [- 3, 3]
• C. [- 5,5]
• D. [-3,5]

Answer 1

Answer: (A)

We have,
$R_1=\left\{(x,y),x^2+y^2\le 25\right\}$
$R_2=\left\{(x,y),y\ge \frac{4x^2}{9}\right\}$
Graph of $R_1$ and $R_2$ are

Clearly, from graph
range of $R_1\cap R_2$ is $[0,5]$.