Question

On the coordinates plane xOy hatch a set of points whose coordinates satisfy the following inequalities in two variables x and y (show the boundary belonging to the set by a solid line and that not belonging to the set by a dash line).
$x^2+y^2⩾1,x^2+y^2⩽16$

Answer 1

R.E.F image

Given in equations, $x^2+y^2\ge 1,x^2+y^2\le 16$ represent circle

with radius 1 & 4 units repetitively Thus can be concluded by

comparing with equations $x^2+y^2=r^2$ (eq. of circle)

for checking area containing origin side or not, test point $(0,0)$

are used

$1)x^2+y^2\ge 1;$ Putting $(0,0)\Rightarrow 0+0\ge 1$ [false]

does not contain origin side

2) $x^2+y^2\le 16,$ Putting $(0,0)\Rightarrow 0+0\ge 1$ [satisfies]

contain origin side

shaded x origin gives the required set of points

Boundary points

$1)x^2+y^2=1$

$x$	$0$	$0$	$1$	$-1$
$y$	$1$	$-1$	$0$	$0$

2) $x^2+y^2=16$

$x$	$0$	$0$	$4$	$-4$
$y$	$4$	$-4$	$0$	$0$